1. Why not pay to compressed public key, without any hashing?
2. Why not restrict it to only valid public key coordinates, to have all existing UTXOs always "mathematically spendable"?

In case of hashes, it is possible, that some particular value could be simply unreachable, and then you won't know, if a given UTXO will ever be spent or not.

As I said in some other topic, if I would want to create a new altcoin from scratch, then it would be based only on public keys and signatures. Because it is possible to add a Script later, just like TapScript is connected with the Taproot public key. Which means, that a new chain could contain only public keys, and operations on them (for example: a signature is a relation between two public keys, formed by addition and multiplication by some known numbers; in general: R=Q*first+second, both for classical ECDSA, and for Schnorr signatures, just different formulas are hidden behind "first" and "second").

Which means, that if you have some P2TR address, and you spend only by key, then multi-signature can work fine on top of that. In case of sidechains, they could be based on top of any scripts, including N-of-N multisig. And if by "inheritance" you mean applying some kind of locktime, then it is outside of the Script, just as the last field of the transaction. Also, in case of Segwit, if you create things from scratch, then you don't have to include signatures in transaction hashes (but unfortunately, Satoshi put that model even in the whitepaper, but for new coins, built from scratch, they could have separated signatures from the very beginning, for each and every transaction; and also that new altcoin could make hashing a transaction much easier, than it is done today by "FindAndReplace" or by Segwit/Taproot partial hashing of some chunks, and combining it).