A really rich mix will make it hard to start. More modern engines will be worse, but it won't really hurt anything, synthetic oil and leaner mixes obviously being less of a problem. A 50:1 mix might increase pollution but it would probably be no worse than running a few ounces of Marvel Mystery Oil in the gas.
It really isn't that hard to keep a seperate container though. I have an old Lawnboy which I run at 32:1, I just use the same mix in my McCulloch 440T chainsaw ("The Professional" as I call it), my string trimmers and my leaf blower, most of which call for 40:1 or so. Its a little rich and they might be a bit harder to start. "The Professional" smokes like Texas Chainsaw Massacre on that mix, but it runs fine otherwise. I cut some massive logs with it and while I filled the yard with smoke I noticed no problems, on cooler days it requires a bit of carb cleaner for the initial start.
I actually have a proportionally large amount of 2 cycle equipment and only keep the one gallon mixed at 32:1 regardless of what is called for and run that in all of them and mix more as needed (mainly because the Lawnboy will see the majority of use) and I really can't have a few gallons of close mixed fuel around for less frequently used equipment.. At current count I have the Lawnboy, the chainsaw, 3 string trimmers, the Toro s140 snowblower (more like a gas version of an electric shovel) and the leafblower. I may even buy a gas hedge trimmer but I'd use the same mix.
I may, if I needed to get rid of it, run extra two cycle stuff through the 11hp Briggs IC engine on "The Beater", a crappy Agway tractor I picked up mainly to help in the disposal and removal of fall leaves.