Why are USB hubs mostly 4- and 7-port
Solution 1:
If you're tying up one port to only really gain two, why do it? 4 port hubs are common, and an seven port hub is simply a doubled up four port with one port gone because you're using it to extend the four port again.
It's cheap manufacturing.
Solution 2:
The reason is twofold:
Four-port hub is a mere manufacturing and user convenience. There are one-port hubs (as in active USB2 repeaters), two and tree-port hubs (mostly in "mobile" segment). People also mentioned 5 and 6-port hubs.
7-port hubs are due to specification constraints per single hub. While USB specifications allow for N ports per a single hub, the hub status change reporting is in bit-wise format, and the endpoint reporting granularity is defined as 1 byte (8 bits), see Section 11.12.4 of USB 2.0 Specs. As result, designers/manufacturers limit this reporting map to 1 byte. Upstream port is always Port0, which leaves only 7 ports for downstreams.
If you see more than a 7-port hub, it means that it contains two (or more) cascaded hub ICs inside the box.