It's possible that the government thought that if they did try to challenge the Commerce Clause analysis, then the Supreme Court could have struck down Filburn. They'd much rather lose narrowly on this specific case than have Filburn reversed entirely.

SCOTUS did a pretty hilarious soft "strike down" of Wickard where they basically determined the gun free school zone act (GFSZA) violated interstate commerce clause. So congress just added "in interstate commerce" to the GFSZA and now it does the exact same thing even if there was no interstate commerce involved, and nothing involved ever crossed state lines or actually entered interstate commerce.

So SCOTUS basically solved this by saying the law had to say "in interstate commerce" but it is basically just there as a talisman to ward away challenges, a distinction without any difference as it becomes a tautology.