No. Glider [sailplane] pilots routinely do, but only because of their habit of soaring together in thermals, and the increased risk of a mid-air collision. Larger and much newer (i.e. more expensive) general aviation aircraft sometimes have a "ballistic recovery system" fitted where the whole aircraft has a parachute -- Cirrus a/c are famous for this. Other than that, pilots dropping skydivers use them. And in some jurisdictions, aerobatics. And that's it.
General aviation is about as safe as riding a motorbike. You're trained to not get into that situation in the first place -- it's a very fishy video for many different reasons. We plan for eventualities! Pilots assume that everything _will_ fail and ideally don't let themselves get into a position where a parachute is needed. I've been in a glider (ASK-21) under tow from a tug plane (a Piper Pawnee) where it lost an engine cylinder at exactly "the worst point" on the way up. The pilot waved us off immediately, and we both executed our well-practiced "eventualities" plan for that airfield, with no incident whatsoever. An investigation showed that the engine casing on the Pawnee had cracked, despite recent inspection.
General aviation is about as safe as riding a motorbike. You're trained to not get into that situation in the first place -- it's a very fishy video for many different reasons. We plan for eventualities! Pilots assume that everything _will_ fail and ideally don't let themselves get into a position where a parachute is needed. I've been in a glider (ASK-21) under tow from a tug plane (a Piper Pawnee) where it lost an engine cylinder at exactly "the worst point" on the way up. The pilot waved us off immediately, and we both executed our well-practiced "eventualities" plan for that airfield, with no incident whatsoever. An investigation showed that the engine casing on the Pawnee had cracked, despite recent inspection.