That's what Frostr does.
My assumption is that it's worse because it creates this requirement on all clients, while the Promenade bunker works anywhere with a generic interface. It's faster also in theory because signers are already connected directly to the coordinator.
See nostr:nevent1qqsqqq8klshrth20jlzpu9c9t0m3j3qqqudk5s7ndn3ltjyztqaghuqpr9mhxue69uhhq7tjv9kkjepwve5kzar2v9nzucm0d5q35amnwvaz7tmrdpex7mnfvdkx2tnyw3hkummw9e3k7mgzyqalp33lewf5vdq847t6te0wvnags0gs0mu72kz8938tn24wlfze6wm5a5u
But yes, if everybody agreed and all apps included this coordinator then it would be technically better. We'll need a strong standard for it and bully everybody to support it.
