Can't be too safe. That strap may be what saves you and the now very nice Jeepster. I work alone mostly as well, but my phone is ALWAYS on me (not on a table nearby as that is useless unless you can reach it).
I've seen cars come off a lift for many reasons from being in too much a hurry (most common), another the air cylinder seal gave out in an in ground 2 post, and yet another an arm cracked, dumping the BRAND NEW (sold just that AM and with customer watching) 1980 Cadillac Eldo Brougham over and onto its side-ish, crushing his Snap-On toolbox narrowly missing the mechanic in the next bay. Another 2 post lift there sagged while Geoff (mech) had his hand above the trans installing a bolt trapping him as it slowly came down crushing his hand between the trans and firewall. The next week George McCaddon (owner of the dealership) closed the shop then pulled all 14 lifts and replaced them with new. That was a great man to wok for.