Taping on wirenuts at best is pointless and creates a sticky mess for the next guy and at worst, it holds on a loose wirenut that shouldn't be loose and should be fixed.

If the wirenut is connecting two or more wires together, you definitely don't want loose wirenuts so it would be better if the wirenut popped off while you were pushing it back into the box so that you can fix it vs loosely holding it on with tape so that it 'looks' okay and having a bad connection. But ideally, you should be confident enough that you did it right so that pushing it into the box doesn't cause an issue in the first place. After putting the wirenut on, tug on it and tug on each individual wire. None of them should move.

I guess there's no big harm in taping a wirenut onto a single wire. But I'd prefer that you get a properly sized wirenut that won't come loose on a single wire.

Ok, this is the answer I was looking for! I guess I'm off to Lowes later to get some nuts sized for single wires. The other nuts felt snug, I just taped them up for extra security.

Sam- That’s the right call. Get several sizes of wire nuts so the single ones are secure and so that you also don’t have any where the wire nut is too small to securely hold several wires. Most packs of wire nuts have charts that tell you have many wires of what sizes fit into different wire nuts.