What do you think its primary purpose should be?

1. No mempool. I agree with Gmax' argument that blocksonly is a perfect mode, for "leaf" nodes ¹. Also, I feel that while a properly running relay node may help, a badly configured one or low-capacity node doesn't ². If you're just looking to do your own validation of (low volume) utxos, no mempool is the best mempool, as you anyway don't want to zeroconf.
2. Knowing what's going on with your LN channels (or other pre-confirmation risk monitoring). Like I said above, for watchtowers you want to know as much as you can, even stuff that is unlikely to get mined ³. This is technically more permissive than being a reflection of what gets mined, especially when we see pool / template decentralization.
3. But we do need relays also without LN, because hub-and-spoke would be bad for centralization. For this, I'd say the mempool is basically your pre-validated set of transactions that you pass around, like a hot database of what you want to relay to others. This is the use case where - although not necessarily useful from where I'm sitting - filters could make sense if an operator feels strongly about it. Since someone filtering important transactions is a threat scenario that needs to be minimized no matter what, it shouldn't be too much of a problem when other operators do this.
4. Edit because I forgot: And as a stage for mining of course. I wouldn't filter my mempool if I were a miner/pool, but I'd definitely look to filter my inclusion rules.