Hmmm...I guess I've no firm opinion on this but that which works for me.

I invariably use a strap with the mandolin because I just can't hold it without one, sitting or standing. Usually I use a strap with the electric guitars because I prefer to stand to play them. Acoustic guitars, which I play more than any other instrument, usually have a strap on them but I don't often wear one while sitting, though I don't think I've a preference either way. Often during lessons I use the back of an instrument, by simply flipping it face down on my lap, as a writing surface, so a strap gets in the way then. (This can be hard on the back finish so be careful what you write with etc.)

The issue for me is that I don't like to support the instrument with my fretting hand (because it limits technique) so a strap is necessary while standing or with an instrument which won't stay on my lap. The few times I have a banjo in my possession (I wish I'd bought that Orpheum #1) I have to use a strap because it won't balance otherwise.

There is no right or wrong with this, just what works for you. I always advise to try a strap and to own one just in case, but that it's not necessary.

Mooh.

P.S. Strap tips: I like to leave the strap on the instrument when it's hung on the wall so that's there's something between the guitar and the wall surface which may be rough or cold/damp. When not in use I hang each strap from a strap button screwed to each guitar hanger, so that it's got a home which protects the guitar from the wall. Some strap materials, nylon particularly, may react with some finishes, so leather is a safer choice for straps.