If you're smart, you know how to plan out the triggering of the pod in such a way that you have a way of dealing with it.
Yeah, we all figured that out back in EU with slow movement and overwatch. You poke your way into the darkness, triggering only one group at a time, and take them out as fast as you can. But now you can't do that. Now you have 8 turns to cross a map. Which you can deal with, of course, but it means taking more hits, more casualties and generally having a harder time of things. Which, considering that in the beginning a single hit is the type of injury that puts you out for an entire month, is not the sort of setbacks that are easily dealt with.
Not to mention that stupid "Shaken" mechanic. Because I really needed another reason for my units to panic for no reason. Not like I don't have 3-4 sectoids getting cross the map mind control attacks every mission.
Time limits are there for exactly the reason people hate them, to pressure you into moving onward and to force you into making decisions on the fly (as much as you can given the turn based nature of the game). It's there to prevent you taking part in extended firefights that EU was known for and force you to make risky movements.
Again, adapt to it or lose. Tactics from EU don't work anymore and it's time to do things differently. By which I mean liberal use of grenades. All day, every day. Or avoid engagements and try to hog concealment for as long as you possibly can.
Basically the timer forces you to avoid extended firefights like the plague, which means you need to plan your firefights in advance and only break concealment once you're certain you can take out the enemy squad in a relatively short timespan, or until you're close enough to the objective.
Turn Based Strategy as a genre is built on cheaty AI bullshit. Praising some cheaty AI bullshit while mocking other cheaty AI bullshit just betrays a fundamental lack of understanding how the genre works.
But generally the cheaty bullshit isn't front and center in your face. It's generally the AI having more health, more units, better aim, full map visibility, that sort of thing. And thats fine because it exists to deal with the fact that the AI can't ever be as resourceful or effective as a human player. But this extra movement thing is annoying because not only is it right in your face all the time (Ah! you saw me! I get to move! Now I move again! Hope you like shock lancers because here's 5 of them right up your butt from half the map away!) but it's a bandaid solution for a deeper problem in the way they spawn enemies. There are many other ways of handing it that don't involve cheating, or as obvious of cheating. Thats the big problem I have with it. I understand the reason it exists, but I also understand that it could just as easily be replaced with something less annoying.
It's not so much a bandaid solution as it is a very deliberate mechanic on the developer's part. It is a way of cheating to give the AI a slight upper hand in order to force the player into adapting their strategy. it's how all TBSes do it, they cheat so the AI always has an initial upper hand on the player.
Now, combat in nuCom is mostly based on positioning rather than pure stats. While stats still play a role there's obviously emphasis on the former rather than the latter(given how visible the effect of flanking is). So, how do you skew the odds in the AI's favour? Well, you start off with the traditional TBS approach of giving the AI more health, numbers and damage output than the player.
However that doesn't mean jack diddly squat because of how important your position relative to the enemy is (those goddamn flanking shots). You can have the meanest, toughest, most numerous bastards this side of the galaxy and it won't mean shit if they're all in a visible position with no cover because of how flanking works in nuCom.
So either you completely redo your entire combat system to make cover and positioning less important, which isn't really an option, or you find some way of negating the quite frankly staggering advantage the player has over the AI when the AI is flanked.
Whatever you do to solve this problem, it's gonna be cheaty bullshit on some level. Overt, covert, it really more depends on how you choose to perceive it than on any fundamental mechanical level. People think it's bullshit that the aliens move when a pod is discovered, and that's fine. But make no mistake, every TBS game ever made is full of similar tricks, some just being more covert than others.
Anyway, my main point is that nuCom is a different type of TBS than oldCom was, much in the same way that Starcraft is fundamentally different to SupCom. They have a different way of doing the same thing and comparing one to the other is more of an apples and oranges thing than most people would care to admit.
Re: cheaty bullshit: I think the point of the matter can be seen much more clearly with just the simple idea of classes and abilities. XCOM is not a realistic tactical battle game. It's a turnbased tactical action-RPG, with everything that entails. Turn order matters little when you have ability combinations allowing you to empty a double-size magazine of a sniper rifle, all equally precise shots, in the span of a single turn. Silent Storm really had it right in all respects. I keep saying it, but it'd make a wonderful platform for an X-Com sequel. It just does so many things exactly like X-Com needs, strategic gameplay aside.
Especially with the destructible terrain in that game. Explosives were so much fun.
Also I'd argue that any semblance of "realistic" goes out the window whenever you try to do a turn-based strategy. Unless it's a WEGO type thing. Or you do it pausable real-time like the UFO: Afterblank series.