but the next thing I do is mute it and stick it in my bag in the back seat.
Better in your pocket or a fanny pack you're wearing than in the back seat. Two reasons:
Though not so much a factor in a landplane than a seaplane, it is still a slip possibility that following an unusual landing, you're getting out as fast as you can. When this happens ('been there) only things on your body are leaving with you, things in the back will remain, as you won't take time to go digging for them. For the effort to have your cell phone on your person, you may as well, so if you ever have to call for help following a crash landing, your phone left the plane with you, rather than burning in it. A friend had an in flight fire in his 182 amphibian last year. The plane was on fire as he landed it, happily on a runway. He got out - just - the plane burned to the ground, with everything he had left aboard as he rushed out. Or, worse:
You crash, and are trapped in the wreckage. You want your emergency resources within reach from your seat, not out of reach in the back. This happened to a friend decades back, crashing a Cherokee in Labrador on a winter night. All of his comprehensive emergency kit was behind the back seat. He was pinned in by his ankle, and could not access anything to keep warm, or to communicate. His ELT went off, which helped him be found - very good. However, it had no remote switch, so he could not turn it off, when the rescue helicopter was radioing him on 121.5 hovering above. He could hear them calling, but the airplane radio he was using (broken antenna, I think) could not transmit over the ELT, so he could not transmit his condition and other information to the rescue crews. Therefore, my planes also have a remote ELT switch, not only so you can turn it on, but also so you can turn it off! When flying solo, I carry all emergency gear within reach of my seat. For water flying, I wear a lifejacket with large pockets built in, with a summer night's worth of emergency gear in those pockets.
DAR, this may have already been asked... but when are you going to write a book?
I have about 100 pages written down along the way. One day, I'll figure out what to do with it.... In the mean time, PPRuNers get bits of it on the installment plan!