Are there Instrument-only airports?
No.

Think about what you are asking.

Scenario:

You're a captain at the pointy end.  All your instruments have failed.  Maybe let's add in some extra emergency element for good measure.

You need to land at the nearest usable airfield using little more than the good old Mk1 Eyeball.

Your concept of an "IFR only" airfield can shout "IFR only" down the radio all they like until they are blue in the face.  But in line with the rules of the air, the captain has the ultimate authority, if he's got clear VFR, he'll be landing there as he has no other options.

Keeping the spam-can brigade out of the way of busy airfields is not the job of airfield policy, its the job of airspace policy. And that works perfectly well.

Conclusion:

Even if they might be rarely used on a daily basis, having VFR procedures in place is important whether you are a major airfield or some grass strip.

That way, everyone knows what is expected of everyone else.