If Bandai one day decides that mechas stopped being popular enough for them to simply have one for that year; then we will totally see a new team without one; kinda like how we stopped having teams with motor vehicles.
Motor vehicles disappeared because action figures sales lost importance in Sentai's toyline. Nowadays, almost every equipment Sentai get is either for the mecha or things that can be used as roleplay toys. The vehicles fit in neither class, and so were mostly forgotten.
It seems like that ship sailed a long, long time ago - if there was ever a chance of that happening before the current crossover-heavy era, there's no chance of it now. You can't have your brand new team hanging out on the ground with Goranger while 30+ teams stomp around with big robots.
I don't think the crossovers have much to do with it. Past mecha rarely seem to appear there, aside from the Vs movies, and they could put both teams in a single mecha there. The real reason it won't happen is toy sales.
Like said above, for Sentai, action figures of the actual Sentai members are a fairly minor part of the toyline nowadays - to the point that, for example, Kyoryuger's toyguide for the 1st quarter didn't feature KyoryuCyan at all. The toyguide had his batteries and mecha, but they had nothing for the actual KyoryuCyan and so his existence was a surprise. Cyan, Gray and Violet had no part in the main toyline due to how disinterested Bandai is in pushing action figures. Of course, later they got keys and other things, but that's already merchandising for fans, not the ones that are advertised on tv right alongside their debut.
The lack of importance (and sales) of Sentai action figures is why vehicles mostly disappeared too and we started getting more and more mecha to replace them. Bandai likely doesn't have much interest to fix that either since Rider's toyline is filling that niche recently - and Sentai likely would need to be heavily redesigned to get an actual action figure push. You can't have something like Gaim's swappable armor or OOO's combining system with primarily spandex based designs.
All I want is for the clusterfuck-prone mechs to come to an end. Maybe they could have a non-combining robot like Galaxy Mega and have a gimmick where it can switch between "armors" based on each of the ranger's powers and such.
We aren't really getting "all mecha combine" anymore like we got with Go-onger and the shows right after it though. The main issue is just that the mecha suits in general seem very bulky nowadays. They don't seem to be designed for mobility at all.