As far as jobs for instrumental music players (no vocals), they are certainly less in number than those for vocalist/players, but they are there...I worked for over 11 years straight doing instrumental music (using an Arranger Keyboard), in my case, at a high end restaurant.
In that environment, vocals aren't wanted, as they interfere with the conversations among the patrons; vocals command more listening attention, rather than supporting the activity happening at the venue.
Yes, that corresponds to my experience. There are a number of locations and occasions where the music is expected not to disturb conversations of the guests. I have heard a lot of people complain about entertainers on birthday parties because the music with singing was too loud and impeded conversations. There are also events such as stand-up receptions (e.g. directly following a wedding ceremony) where just live high-quality background music is wished. However, such people rather want to have a pure pianist, and it seems to be difficult to offer them a digital symphony orchestra played on the keyboards instead. So I'm currently offering both pure piano music and orchestral sounds.