Balance Question: "One Kit Ever"

I'm curious if the following proposal could be broken -- more overpowered than the options we have now.

Here's the proposal:
- Characters may select up to one kit ever.
- When you dual-class, if you don't have a kit, you may choose to gain one in your new class.
- If you have a kit when you dual-class, you may only dual into a base class.

For the purpose of this proposal, let's say Sorcerer counts as a Mage kit. So, you could have:
yes Fighter > Swashbuckler
yes Kensai > Mage
yes Fighter > Sorcerer
yes Fighter > Avenger Druid
yes Berserker > Druid

But you could not have:
no Kensai > Sorcerer
no Berserker > Avenger Druid


In a world where Kensai > Mage is a legal option, is it MORE broken to allow stuff like Fighter > Wild Mage?

Thanks, -- N