As of today there is no wallet (that I know of) that generates Taproot addresses
Bitcoin Core of course does that. And yes, it is a wallet, because it can be used offline to sign transactions, there is no need to download the whole chain, it is just more convenient, because then it is possible to use GUI. So, the lack of GUI features that would work offline, is the only drawback.
because they will spend even less transaction fees
It depends. Some examples from testnet3:
Taproot-to-Taproot transaction, 112 vbytes: fcaa640adf77217288ed40f1d623bd98f09370dbc31013e121ddfa053851e373
Segwit-to-Segwit transaction, 110 vbytes: 2bb9718757e8e550aa48e5af2c41bb1e862b68be270483d6d9b6b162dcbd40a8
However I have not yet seen any wallet that lets you create SegWit version 1 addresses (aka Taproot) easily.
You can try Bitcoin Core v23.0.
getnewaddress "" "bech32m"
bcrt1pt3ugstag3z2mzxech2fwra22usyl72zaxqlm9vh8ue2dee8p0qvsyw6z2x
I don't think it is hard. As I said, the main problem is the lack of GUI features, everything else can be easily done from console. But still, it is possible to run some Bitcoin Core daemon offline, and then connect any GUI-based wallet, that would provide all needed data. If someone does not have a blockchain, it will not be any worse than using some SPV wallet.
Use SegWit version 0 since there is no user friendly way of using version 1 (aka Taproot).
Yes. If you are a user, use SegWit for now, because it has better support. But if you are a programmer, then use Taproot, and base new features on that.