Why don't P2PK scripts have their own address?
One of the issues with encoding P2PK outputs as an address is that they can be very long. P2PK can have both compressed and uncompressed keys. Uncompressed keys are 65 bytes, which means that the resulting address would be very long. In fact, this length is probably why P2PKH exists in the first place: as a way to have short strings as addresses. So P2PK addresses could be very long and unwieldy, so not that useful.

But nowadays, everyone uses compressed pubkeys so length isn't much of an issue anymore.

Since Satoshi didn't give P2PK an address type, the reason that one has not been created since then is that no one cares to. P2PKH already does everything P2PK does, just a little bit longer. And with other improvements coming such as Taproot (which is A pay to pubkey scheme and has its own address type), there isn't a compelling reason to go through the effort of defining a standard and trying to get wallets to implement it.