Budget wasn't really why Supergirl was moved from CBS to CW. Ratings were. It couldn't maintain the high numbers that CBS shows typically do in that time slot. The demographics weren't there. People thought the budget was the problem but it has largely been the same as there wasn't any visual downgrade on the show when it came to season 2 and 3. It would have been noticed. In fact things have gotten better. Same across all the DC superhero shows on the CW. Now that could be because they've just simply refined their technology over time and gotten used to using their budgets more wisely as well but nothing has suggested there has been a drop off in budget on those shows. Not in any big way anyway. They just did a super expensive movie that was a crossover between four shows and do these crossovers ever year.
Supergirl is very likely though why Discovery went straight to CBS AA and was used to push that service instead of even being attempted to be shown on CBS proper outside of the premiere. Demographics were strongly at play..
Right. The CBS prime-time lineup is, what, a bunch of crime procedurals and some low-common-denominator comedies? Plus Madame Secretary, I guess. Supergirl didn't make any sense in that environment