Why not to use mono from kayak

30lb mono is not difficult to break.  Neither is 40lb.  No gloves needed.  Hobie mirage drive makes it easy, or paddles work fine too.

Mono has its applications; trolling and fly lines.  But I never use above 20 lbs for the kayak.  As you said its too hard to break (especially in deep water).  20 lbs mono will easily two your kayak so it not necessary to go heaver then that.
For bottom fishing/jigging, I use braid with a 30 ft topshot as has been said. This way I can just keep trimming the mono leader as it becomes damaged.   Again I dont use above 20 lbs line for the kayak.  You'll need heavy braid if you set up a "Kelp-Cutter" rod, but I dont know alot about them. 
Thats my 2c

You could just learn to break your line properly. If you’re cutting your fingers with mono, you might sever them with braid.

Wrap,your line around around a bonker of gaff handle and get it tight, let the swell lift you and break the line. Retie and you get to keep fishing.  And you get to keep your fingers.  Win/Win

this.  Also, dangle while you do it.  meaning, throw both legs over the side of your yak for better stability. Winding up on a bonker is my technique when I need it.  Plus, I find mono snaps just as easy as braid. I use braid for more line capacity and I can use less weight to get to the bottom.  always have a mono or flouro leader though.  Or topshot If I'm doing that kind of fishing....

Another preference for braid is no stretch= greater sensitivity and quicker, more secure  hooksets.  Having said that, there are applications where braid has worked against me.  I will not fish ocean salmon with braid.  I feels like someone is hitting my rod with a hammer, no streth increases possibility of ripping out the hook.

I tried using gloves but I always lose them.  so when needed, I go with the bonker windup technique.  Rarely have to use it, usually I paddle directly backwards up the drift to get on theotherside of the snag.  I that doesn't work, then I get right on top or the snag keep the line taught, and paddle slowl in a circle basically pressuring from 360 direction. 9 outta 10 snags will release for me.

Don't pull with bare hands even mono can cut you when your skin is wet and soft.

I could go on.......



Bushy

80# braid, excessively strong I know, a three foot shot of 80# test mono which is almost abrasion proof in the rocks, and 40# mono leaders for jigs and hoochies. 40# is the most I wish to break off and I almost always point rod to stern and pedal hard till the leader parts. Heavier leader really helps in getting a big ling out of a hole without breaking off.

I would be afraid I might snag up on the mainline and not be able to break it off.

I use the Crash technique, but wrap the line around the reel handle knob. Then pull with the rod pointed straight at the snag.
If you can get vertical on it often the snag will just drop free

Here's what you can do to avoid snagging bottom and getting stuck with unbreakable line.

Option 1) Use a weaker snap swivel on your weight.

Option 2) Use 15-20lb mono for your leader.

You can land a hard fighting king salmon on 15lb test with the right drag. I'm sure you can land a nice lingcod/halibut with the same line.

15lb line is stronger than you think.

I use heavy mono with big reel. Braid may cut off finger.

I use 30 or 40# braid with a 30# topshot or 15 to 20# mono. Use the jiggle to try and free up the junk, typically get home with almost all my gear.