My thinking is that if you're pissing off the traders to the point that they won't trade, or if you can't scrape the 1000 or so dwarfbucks together one costs by the time you need it, then you have problems beyond not having an anvil.
This is what I was going to say after reading the OP. Glad I'm not the only one who thinks that.
I mean, how the hell can producing a bunch of crafts or one or two prepared meals for an anvil be a problem? If a new player can't manage that, they should read the fucking manual (aka tutorials), as they probably don't know what's going on in this game in general.
It is only to say that the "No Anvil" suggestion is over-rated and should be treated as preference rather then "The way to play". The Walkthroughs I've read treat "No Anvil" as the way to play as well.
It might as well be the way to play in normal circumstances, because spending so many embark points on something most people have no use for during their first year, or even couple of years, is so obscene a waste of embark points that it's not even funny. Now, if you made rules for yourself, like no trading, that would be a different story.
Also, I don't mean to condescend, but I have to point out what I hinted at above, namely that your argument that a new player might not be able to trade for one easily is laughable for reasons already mentioned.
So far most people are arguing that starting without an anvil is a viable strategy when in order for it not to be over-rated they would need to prove that the money you spend with an anvil is absolutely vital and should be used somewhere else.
-Edit addition: Hmm too far... Proving THAT much would change the nature of this topic. Which I already realise I am betraying.
Correction: all we need to demonstrate that embarking with an anvil is, for most players, useless. The fact that most of us here seem to wait a year, or perhaps even a couple of years, before starting a metal industry, is evidence enough of that. I guess your edit suggests that you realized as much yourself, eventually, but I just wanted to point that out.
and this way I don't have to make upteen jillon worthless rock crafts to buy from the caravan, just to have someone else hit a craft mood right as the guy making the crafts hits legendary, leaving me with two dwarves legendary in a skill I would be just as happy to never use.
There's another way of avoiding churning out stone crafts for trade: producing food and cooking it. That's something a player should be doing anyway (unless they have some weird-ass house rules forbidding it), so I don't see what the problem is with doing it right after embark.