My question is: can the game be completed without using Thievery to rip off traders?
I hope your question permits to use thievery to unlock doors and chests.
and yes. I think it's possible.
first: there are plenty of stuff to craft your own gear. also Lucky charm to 6+ will help a lot. we've made more then 100k just with it during act3. and I have no idea how much we've gained through the whole game.
second: trader reset to buy more runes\pots\etc will not go away. also I hope you don't see "selling as much stuff you could then killing the npc to get it back as stealing'. I always though it's common sense.
third: you don't really need to have a gear always up to date all the time. for us it were lvl4(weapon), lvl9(preferably armor and weapon), lvl13(weapon), lvl16(armor and weapon) and lvl20 - go crazy and optimize all your gear with saved money.
forth: some classes, especially casters doesn't need optimized gear. my necromage wore teleportation gloves for the whole game. mainly cuz of teleport-corpse explosion combo. and the only things I cared about were items with sockets and the best shield I could afford. I even used Radeka's wand cuz it gave me 5%crit chance til arks.
fifth: there is a way to cheese some encounters which makes gear less relevant. iirc even the last fight can be cheesed by letting the Lucian do the job for you. you'll just need to keep him alive. though it all depends on your choices.