I knew that by foiling the plans of the archery trainer that he likely wouldn't train me, and I was right!

I decided the gold would be better spent on other things, and that I could practice archery in the wild (which takes a long time).

Was skipping the archery training a mistake?

Actually, I am 1H shield warrior and I find that I can close the distance to archers really fast by running to them an ripping them open with my axe. Havent needed archery.

No probably not. Who is this archery trainer though. I have been looking for one.

If you're 1H + Shield why would you need to train your archery? There are other trainers and I believe the cost is based on the skills level, so you'll still be able to get "cheap" Archery training from the next trainer.

You can train, then steal the gold back

No, it levels up nicely, just remember that Archery is governed by the Warrior this time around, not the Thief.

On the plus of that, if you sneak a lot you'll be getting great skill ups in both Archery and Sneak, as stealth shots split between both, and your Archery gains from Warrior seem to boost both (or Archery up to the level of Sneak, not real sure on the specifics but they stay pretty even).

Also there's a woman way out in the boonies somewhere who will train you, and she also has some target practice challenges that give some easy free skill ups. I think you can actually marry her as well, so maybe even free training.

Archery, at least for me, was a pretty big deal. Especially when fighting giants and dragons from a far distance. But there are always people to train with, there's an elf in Riverwood and there's this lady with the Companions. Hope that helps.

You archery should reach 100 easy.

You should do training for a skill that you want to increase, but one that you don't normally do or there isn't a proactive way to increase it.

E.g., as an assassin that specializes in 1-shot kills, my sneak reached 100 easily, but my one-handed skill is very low. The nature of my combat style means that I end up not doing many strikes to defeat enemies compared to other people, so naturally the skill won't be high.
But I still need a high one-handed skill to maximize my sneak dagger damage. So I should train in one-handed skill from trainers.

If you're referring to the elf from Riverwood, you don't need to steal the gold back, you can simply "change equipment" with him after he becomes a follower.

Free archery training until skill level 50. Archery is slow to level naturally, so this isn't even that big of an exploit, IMO.

You'd think the trainers would run to the bank after being paid 2000 gold, and not keep it on their person.