It is much worse in say the NFL to trade up than in the NBA. The NFL roster size and sheer quantity of talent you need vs. the individual player impact of high NBA draft picks is the main difference. The bust rate is also much lower in the NBA than say a franchise QB. Plus the rookie scale doesn't properly account for the extreme impact of the top players (it scales, but not as drastically as it should).
It's a good idea to accumulate picks to increase your whacks at the pinatta, but what if you've already nailed it? The Hinkie plan is the best for rebuilding, but competing for a title is a different strategy. At some point you need to take advantage of your prime window and draft picks aren't as valuable when veteran stars (who 90% of the time are better than rookies or 2nd years) want to come and win with you and you can sign them in Free Agency at minimum or exception rates without surrendering any assets other than cap space. Additionally, in the NBA having a lot of good is good, but having a couple great is better. Consolidating talent into fewer but marginally better players is worth it.
For the Celtics specifically, it's about opportunity, timing, and certainty.
For opportunity, this year's class is exceptionally loaded with bigs, which is the Celtics main need going forward into the future. They are set for at least 2 years at every other position. If they were going to cash in assets to make a move, this would be the time. The Celtics have the ammo because they have potentially 5 1st round picks the next 2 years. They can't even roster that many first round picks. Sure you can draft and stash, but...
The timing is ideal because they don't have minutes for role players as it is the next few years, let alone with Hayward and Irving fully healthy. How are they going to develop those guys when they can't even crack the top 10 of the rotation? Further, the Celtics roster is currently constructed more in the "a lot of good is good" way. They will be unable to pay all these players because the salary cap is a bitch, so their ideal championship window is the next 2 years. Sure you can draft replacements when those picks convey, but there are few guarantees those picks will be valuable enough to do so at an impact level in a quick enough time to matter.
Unlike the NFL or NHL, the best teams in the NBA win basically every year. There is no "getting hot" or having a hot goalie, etc. The team with the most talent that plays the hardest wins almost every series. As mentioned above, the more elite, elite talent you can get, the better off you are. There is less risk in potentially shortening your competing window if you get yourself the best roster in the league. Whereas in the NFL, even with the best player of all time, it's best to elongate your window and try for as many shots at it as possible.
You're not mortgaging the future by trading excess picks for a pick. It's still giving yourself a future. NBA teams have 7 years of control of a top draft pick, 4 of which are at great cost savings. Say you trade your own this year, the future Kings pick (likely to be in the 5-7 range) but protect it top 1, and the Clippers pick (possibly mid round 1st, downside of a 2nd) to Mavs for #3. You've still got all your own picks and the Memphis pick.