The biggest gripe with Derrick White is 3pt shooting. Before this season, he was a career 35.6% from 3 (over 600 attempts). This season with SAS, he was down to 31.4% (258 attempts) and with the Celtics he is hitting only 24.6% (57 attempts). 24.6% is obviously really bad. I don't know why he is so far below his career average but it is understandable that fans are critical of his shooting since joining the Celtics. Everyone agrees that he has otherwise been really good.
So if he can get back to shooting say 35% from 3, the consensus will likely be that we may have overpaid but that we got a good player on a good contract. If he continues to shoot 24%, this will go down as a bad trade. Maybe it is the new ball or the new defense rule, whatever, he needs to figure it out and start making more shots.
I don't feel that is is unreasonable to expect him to get his shooting back to his career norms or better. That may involve better shot selection. In any case, it is probably premature to judge the trade based on him shooting 24% from 3. That is probably not who he is as a player in the longer run. Didn't Tatum miss 21 in a row or something like that earlier this season? He has certainly had stretches where he has shot in the 20s% from 3 for a stretch of 50-60 attempts (27% in Oct to start the season on 55 attempts for example).