> with a seemingly infinite possible combinations

Verisign claimed approximately 22,000 third level domains [1] in July 2026. I don't see an estimate of the number of shared second level domains, but it's finite. The current public suffix list includes 10414 names [2]; so at maximum, the list would approximately triple in size --- not ideal, but feasible.

[1] https://itp.cdn.icann.org/en/files/consensus-policies/fessen...

[2] including some with wildcards, re: your other post