Why doesn't address contain a full scriptPubKey?
There are several reasons for this, some historical and some more recently:


At first, addresses were probably not intended to cover everything Bitcoin Script could do. They were a fallback for the case where the recipient was not online (we're calling addresses still addresses because they were originally IP addresses you'd connect to to request a scriptPubKey). So at the time they were introduced, a focus on size was probably far more relevant than considerations about flexibility. Note that addresses have a 'version byte' (which was intended for upgrading the format, not for identifying altcoins).
Later, when P2SH was introduced the concern about flexibility went away entirely: P2SH permitted conveying any spendability concern in a constant-size address. Furthermore, it removed the concern of senders needing to create larger outputs. The fact that I am using a multisig wallet shouldn't mean you have to pay a higher fee when sending to me.
When SegWit was introduced, P2SH was no longer sufficient to encode any output, for reasons of efficiency and security. Despite the need for a new format anyway, we still chose not to propose something that could encode arbitrary scriptPubKeys. The reasoning given in BIP173: 


Why not make an address format that is generic for all scriptPubKeys? That would lead to confusion about addresses for existing scriptPubKey types. Furthermore, if addresses that do not have a one-to-one mapping with scriptPubKeys (such as ECDH-based addresses) are ever introduced, having a fully generic old address type available would permit reinterpreting the resulting scriptPubKeys using the old address format, with lost funds as a result if bitcoins are sent to them.