Ii disagree. i think the end of season is the best time for team training (ft and stamina; not game shape because it will be reset at the start of the new season).
For these reasons:
a) you are training good players too, it is not wasting; and these two attributes usually pops quicker
b) assuming you would train ft/stamina sooner or later so why not now
c) it is probable that ft and stamina won't raise salaries as much as improvemen in other attributes do and we are just before a raise of salaries (at thestart of the season - once per season)
d) there is a lack of matches so it is more difficult to get 48+ minutes for all your players who you want to train
e) level of a trainer doesn't count in team training
f) he will get 3 prospect from draft and should decide according to what he got (and if he has enough inforamtion and a sufficient position in draft, maybe he should draft accordingly (to get current best candidate for trainng a promising fellow at the same position))
g)fts can be crucial at the ends of close matches and it is good not to have players with atrocious FT at the end of game (luckily opponent don't foul the worst FT shooters on purpose as I can guess but still)
h) he can't discarded all not ideal players now, he has to have some players to play with and counting with some injuries; of course the weekest should be fired (sold) to save some money.
I didn't look at his roster but it wouldn't change much anyway.