For my money, at least, I would hate if the NBA moved its season. Since I'm not a big NFL fan, I don't mind that the seasons somewhat overlap, and I do take full advantage of the fact that the NBA and MLB seasons are generally non-overlapping - I get to watch one of my two sports almost year-round.
But even setting that aside, is football really that much more competition than baseball? The NFL plays 16 games a week, generally 14 of them on Sundays. MLB plays about 90 games a week, somewhere between 5-6x the number of football games and while Mondays and Thursdays tend to be a little lighter for travel days, weekends definitely have 15 games per day and Tuesday/Wednesday usually have 14-15.
Consider a three-sport city with only one team in each sport. Under the current schedule, the NBA starts in mid-October, when the NFL has about 10 weeks left. Teams play less than every other day in the NBA, so you don't expect to play on Sunday more than 5 times (let's say they all conflict with the local NFL team), plus let's say for bad luck you also get a conflict on one Monday/Thursday night. So 6 conflicts with regular season NFL games. Now, we've got the playoffs. We can pretend it doesn't matter who plays in the playoff games, those have an audience even for non-market games. That's three weekends (six days, assume three conflicts) of games plus the Superbowl, which the NBA won't schedule against currently. So, grand total of 9 conflicts with the NFL. Now, MLB starts in late March/early April, let's say that's four weeks of conflict. About 3 games a week translates to another 12 conflicts, because basically every game conflicts, for a total of 21 conflicted games out of 82. Note that those final 12 conflicts are soft conflicts because stretch-time basketball probably beats first-month baseball. Playoffs don't conflict, because NBA playoffs beat first-third baseball.
Now, under a new schedule, going from December to August. Well, you still have 3-4 weeks of conflict with the NFL regular season, but let's be generous and say just one conflicted game. NFL playoffs are the same, so three more conflicts, a total of 4 hard conflicts with the NFL. But now, the NBA runs much more of its season against baseball - 1.5 to 2 additional months, depending on how the schedules are lined up. Let's call it seven additional weeks of the regular season. That's now 11 weeks of conflict and 33 conflicted games. Together with the NFL that's something like 37 conflicted games out of 82 before the playoffs (where the NBA wins, but maybe not quite as thoroughly as MLB is getting towards its stretch run). The NBA has basically doubled the number of schedule conflicts - some of them are softer conflicts (as the NFL is more popular than MLB), but at the same time, since NFL games are almost exclusively day games, the NBA can schedule nights on Sunday and miss the majority of direct conflicts. MLB games, particularly during the week, are night games and you can't try to stagger to avoid that conflict.
Moving the schedule so the NBA plays more over the summer doesn't make much sense to me in terms of direct competition with NFL/MLB.