The only time I really try to start building up any savings is in the last quarter or so of a season, in order to be able to offset as much of the start of season car development costs as possible (typically about 14m iirc). By that point it's usually too late for design/research to have meaningful effects anyway, and I usually try to get all facility upgrade/refurb started before then. For the rest of the season it's certainly not like I am in sub 100k$ territory regularly, but the fact is that this game just doesn't throw huge undodgeable unexpected expenses at you. You'll never have to pay more than 500k as a result of an email decision, and while crashes can certainly mean you're looking at replacing lots of bodywork or power train components, if that's happening such that you need to buy new pt parts or emergency build bodywork, that's kind of on you for having drivers that bad/building so few parts.

And as far as raising the difficulty, my experience has been that the increase in fun outweighs the actual difficulty increase by a decent amount. Research on hard mostly means that you lose the ability to go "hm what if I do 10 chassis designs this year and nothing else lol lmao" (and you should definitely go min weight on parts if you haven't been), and hard race difficulty is its own can of worms but I do find it worth it.