and if you play without trading the game is still designed to be somewhat doable. Really the only thing you miss out on is trading

I don't agree with this at all. Even if you don't want to trade (which only really requires a single premium stash tab anyway) you'll struggle in the endgame if you don't have at least a currency, fragment and map tab. I actually think you need even more tabs in SSF (solo self-found) than in trade league. Because you can't just buy something if you need it you'll probably want to keep way more items. And with the four default tabs you pretty quickly run out of space (in the endgame).

But yes, for the campaign it's not really an issue and I would definitely consider that as perfectly playable for free. And by the time you're done with it you'll probably know whether you want to buy some tabs and keep playing or not.

Tip for people who do want to buy stash tabs: there's a sale every three weeks where all tabs are around 20-25% off.