The junk search terms problem with broad match usually points to one of two things: not enough conversion data, or the account is being asked to do too much too early.
Broad match with Smart Bidding is a data amplifier. If you have 50+ conversions per month with clean tracking, it can genuinely find intent patterns you wouldn't think to target with exact. If you have 10 conversions a month, it just burns budget on garbage because the algo has nothing real to learn from.
For lead gen specifically, my sequence is: start manual CPC with exact/phrase, get to 30+ conversions in 30 days, then switch to tCPA. Once tCPA is stable for another 30 days, test adding one broad match campaign alongside separate campaign, not mixing match types, with a healthy negative keyword list from the search terms you've already seen convert. Never go all-in on broad until you have that baseline.
The mistake most people make is flipping to broad too early because Google recommends it in the interface. Google's recommendations optimize for spend, not for your ROAS. Their recommendation to switch to broad comes the moment an account has any data at all, not when it actually has enough.
Also worth checking: if your search terms look like junk, verify your conversion tracking is firing on actual qualified leads and not just thank-you page views or soft events. If the algo is learning from low-quality signals it'll find more of them regardless of match type.
Exact/phrase for control, broad as a separate test after you've earned the data for it. Thats the order.