Yep, it's useless

The text of the Eldritch Invocation is pretty clear...you can cast bane using a Warlock Spell Slot.

If you don't have Warlock Spell Slots, you cannot cast it. This same rule applies to a multi-classed Warlock: they have to use a Warlock spell slot for this, they can't use a normal spell slot that they acquired from, say, Multi-classing Sorcerer.

The language used across these Eldritch Invocations is very consistent. If it was intended that you could cast these spells using some other Spell Slot, then it wouldn't specify that you had to use a Warlock Spell Slot. It would instead say something like...

You can cast bane once using a spell slot.

But it doesn't. It would have been very easy for them to leave the specificity out, and they did not. Thus it's a safe bet that this is intentional.

This is supported by an interview with Jeremy Crawford (lead rules designer for WotC), found here. To transcribe...

Bart Carrol: "So, for example, if it requires a warlock spell slot, then in that case it would require a warlock to be able to use it?"

J. Crawford: "What this feat is saying, is that it doesn't matter what the prerequisite is. If an Invocation has a prerequisite of any kind, only a Warlock can take it"

While not a definitive ruling (as it's just an interview, not a formal Sage Advice post), and is using Crawford's usual circuitious language...I find this to be fairly strong support. Crawford appears to consider "you need a Warlock Spell Slot to cast this" to be a prerequisite.