I don't think limiting swipes will fix it - the issue is more on the selection side (who women choose to swipe) than on the seeking side.
The reason men swipe a lot is because even with that most get few matches (~0). If you limit their swipes then most will never get matches and they'll stop using the service.
Bumble solves little, many 'initial' messages from women are ".", "hi", or ":)". It's basically equivalent to a match where the men have to initiate contact. The pre-selection winner-take-all issue is still there.
I think you can't fix it via apps - because the issue is upstream sexual selection that's been in place for thousands of years. It's good to have an honest view of it though because it lets people navigate it rather than becoming bitter and miserable.
Even if you had an app where men make profiles and don't swipe at all, one where women just select people and then men get notified - you still end up with only the top 2% of men getting selected and women would have to notify someone they're interested who may not have mutual interest or message them back (a rejection of the type mutual swipe matches are supposed to avoid).
Also, I think at least some women like having hundreds of matches because it's a nice self-confidence ego boost (I think complaining about this is 'high-status' humble bragging). If you took that away I suspect they'd also use the service less. Most women don't want to actually be the pursuers (a lot of men don't want to be either probably, but don't have a choice) - sexual selection doesn't work that way among most other mammals, humans are probably not an exception. If you try to force it with an app I'd doubt it would work.
So this doesn't solve the underlying issue, and economically wouldn't work because men that drive income for dating sites wouldn't have much of a role to play beyond creating an account and waiting (even though functionally this is basically the action they're doing anyway for the most part on the other services).
Men need to play to their strengths - online dating turns you into a commodity competing entirely on looks. If you're not going to win in that arena (and 98% won't), get out.