Okay let's replace PoS consensus-by-betting with Satoshi's PoW. So the problem remains every full node needs validate every script. If we instead split validators into partitions, then they can't all agree on adding the other partitions to a block unless they've all validated all the scripts thus destroying the scaling advantage of having partitions. If we could assume the partitions can't impact each other in terms of incorrect validation impacting the output a script which impacts the input of another script in another partition, then the partitions wouldn't care to validate each other. But I showed that with scripting, it is impossible to know whether scripts in different partitions impact each other. The externalities that the block chain can't know means it can't guarantee the partitions are bounded (i.e. self-contained).
In short, if the partitions can impact each other, then all full nodes much validate/verify all scripts. Thus partitions are useless for scaling.
Partitions in PoW are bad because the hashrate of the entire network gets split by the number of partitions, meaning each individual partition is weaker than the whole unpartitioned network would have been. In fact, the strength of the network tends towards 0 as the number of partitions tends towards infinity.