Making "mining" cheap, and speeding up the network, were originally supposed to be one project, but got split into two separate efforts so that PoS could be shipped sooner (and so stop consuming half the world's supply of GPUs + 0.1% of all electricity sooner.) Gas is still expensive because "space for transactions in a block" is still a scarce resource, because blocks are still only being produced once per 10 seconds.
And they can't just flip a switch making it go N times faster right now, because transaction execution is a serial bottleneck — a "full" Ethereum node can only evaluate transactions at the speed of a single pinned CPU core, and the average CPU's single-core performance isn't going to become orders-of-magnitude faster any time soon. So there is currently a fundamental limit on how many transactions the network can execute per second, regardless of how they're packed into blocks. (And also, even if there was no such bottleneck, the per-node chain state would also then be growing N times faster, which causes its own scalability problems.)
Sharding will fix both of those problems, making the chain into N independent shards where any given "full" node only has to sync some reasonable subset of said shards, and where a node syncing multiple shards can run those syncs independently in parallel (and so — presuming a large number of shards — can use as many CPU cores as are available.) But sharding is not done yet. So gas fees remain for now.