Another hidden benefit of requesting/donating is that it's made so you can just buy a card if it's in your gold shop for someone, donate it, and profit.
Commons get you 5 gold a donation and you buy the first for 3, the second for 4. So it's 3 gold and 2 experience profit, simply by fulfilling a donation request from your store. That's if you REALLY don't have the cards requested, but the store does.
A Rare gets you 50, but you buy it for 40. 10gold and 10(or 5?) experience profit, for five seconds of work.
This matters a lot earlier on, because you don't need much xp to go up a level, and bigger/better towers are good. But you might not have a lot of cards to donate. Buy them if you can, just for the xp (even if you make a loss on the donation). On a Sunday your store is twice as big, so heaps of stuff gets traded between a 50 member clan, regardless of whether they use that card or not. There's really no excuse not to donate every time you see a request, because you do profit in the long run. Even if you and a friend just swap a card back and forth. I tend to say what is in my store in guild-chat, so people know they're on to a sure thing for requests when I'm on (they usually are anyway. My guild knows how the donate system works. You should always donate, it's in your best interest to). The higher arenas your guild members get to, the more likely it is that they'll be able to fulfill your own donation requests, so always donate whenever you can to help make them stronger.
It's both
generous and self-serving. But arena 1-2 commons/rares are good throughout the whole game, so you can always request something worthwhile, no matter your level/guild size/average guild arena level.
It's pretty common that I hit my donate timer, just due to random requests at peak times. I tend to buy 1-3 rares and about 5-10 commons a day, just because. If you could buy a golden chest for ~75-250 gold, you would. I essentially do this every day from the gold shop, unless I'm specifically saving to level something up. Even if I don't use them now, or they're crappy cards, I might use them later, or just donate them to whoever. It also helps you "even out" your cards quicker (I'm not sure if you even have to pay to level them up, or just need the option to do so), so you're more likely to get the cards you actually want to level-up from chests. You're more likely to get epics as well, the more commons and rares you have "an appropriate amount of".
To the question of "can it be free-to-play?". Yes. It's free from the word go. The core experience doesn't change much, and from about arena 3 or 4 onwards, you'll have plenty of cards to make whatever deck-style you like. With the focus being on placement, counter-plays, pushes and defense, a card level or two doesn't matter too much in who wins and loses. Big cards make it easier, but it's not an auto-win. I've pipped people in my clan with higher cards, and the same has happened to me against lower ranked members. Big cards are a crutch, not an "I Win!" button. Strategy and deck focus will see you through. Having different cards is more about deck options, not really deck power (although some cards are still "better" than others, the devs seem pretty heavily focused on balancing them). And you auto-magically get more powerful as time progresses, just by free/crown/normal chests and donation requests. It's just a time thing, not a skill thing, that gets you more powerful. Unless you're hopeless, you will slowly float up through the arenas due to your cards getting more powerful than those in "your bracket". This doesn't mean you're "a better player". There's awesome players in arena 2-5, so have fun playing against them and learning from them. They may float upward a little quicker, but gameplay at all levels is often better than what you see on TV Royale. Easier to learn from as well.
That's the main thing I like about the game. You can have a good, fun game, no matter if you're just starting or have been playing for months. You have to get into a totally different mindset for Clash Royale. Higher level or higher cards doesn't necessarily mean better or more skilled. You've just got to enjoy the ride, enjoy the matches, enjoy the game, and ignore all that. Learn all you can about playing, and you'll defeat plenty of higher level opponents. But your trophies and arena level really don't matter too much, your card levels are a crutch that often make wins less satisfying, and the core experience is exactly the same from day 1 to day 300.
If you like that experience, then you can play it for free. I have been, and I've gotten plenty of epics, good card levels and reasonable towers, and I often only play a match or two a day, sometimes none for days. I just log in, collect my freebies, buy a few cards for gold at the shop, and donate whatever my guild is requesting. I'm level 7 on my towers, most cards are level 6 on commons, 4 on rares, 1-2 on epics (waiting to choose which ones I want to upgrade to lvl7/5, because it's 1000 gold to) and am about to go into arena 5. I'm not particularly good, or very fanatical or hardcore in playing, yet here I am. I've been playing for about 4 days from before proper-launch (about 2 months? or 1 month? A while, anyway), really casually, and am competitive against anything in arena 4 while dribbling up to arena 5. It's a very competitive game, but you can be competitive while playing casually. I like that. I'll probably be playing this game for ages, on and off, because it's fun at "all levels of play".
Sometimes I'll play a tonne of matches in a few days, sometimes a handful in a week. Levelling f2p slows down/gets pricey enough that everything will end up at about lvl7-8 (4-5 for rares) for ages soon, but most of my guild will be about the same. Regardless of how good you are. Yet we'll all have plenty of cards to make more or less whatever deck-type we choose, just for funsies, with strong enough cards to "be competitive". That's free-to-play, I reckon.
Within the next month, things like trophy counts might actually mean something, at around arena 5-7. Because everyone will have levelled out into the "takes an age to level cards f2p" plateau by then, and skill won't be about higher level cards. Cards will do their thing, and a lvl or two won't make something too-squishy/too-powerful, or create huge game swings even with suboptimal play. I can see arena 6-7 (lvl 7-8 commons/lvl 4-6 rares being average "easy entry requirements") being the real skill decider area in the game, but you'll naturally float up near to it eventually. Arena 4-5 just happens, 6 and 7 doesn't. There's enough deck types and enough play-styles at that level, that being "good" will actually require a lot of knowledge and skill, not just time to get better cards. It probably takes 2-3 months all up to get there, then shit gets serious
Of course, as more of your guild members float up to arena 4-5, you'll all have more card types to donate/buy/open, so each new set of cards shouldn't be too hard to get to a decent level pretty quickly. The early lvls are quick as, and Clash Royale likes "evening out" your card levels with chest openings, so you always have the option of being pretty competitive in any bracket fairly quickly, even when exposed to new cards. Chest opening cards aren't completely random, and the first card lvls are cheap and quick to get, so you'll ping-pong between arena tiers for a few days until the new things are lvl3-5 or so (if you're using the new stuff). Quicker if you've got a guild with a fair few members in around that bracket. But I think arena 6-7 will be the real skill-test wall, 4-5 is easy enough to get to.
And yes, skellies are awesome. They block, they draw troops, they add weight to pushes and defense, they add to dps, and they cycle your deck quickly (their best advantage). They might not scale too well, but since they do all the above for 1 elixir, they don't need to. They're amazing.