Perhaps I'm misunderstanding the term but I don't think what I described is split DNS. Split DNS is when the same DNS server resolves a name differently depending on the IP address of the client.
In the scenario I described the DNS servers involved do not discriminate, they always resolve the same names the same way.
The ability to discriminate at the client (to search specific DNS servers for specific domains) is not split DNS (although it's often incorrectly called that).
If this is what you meant then yes, it can be a bit of a headache. For example if you need to resolve local LAN names (.lan or .local), Tailscale names, and Docker names at the same time inside a container it can get a bit hairy.