Not my experience though- I lowered my XT triple mech by a fair bit, certainly more than a few mm and had no chain rubbing issues on either bike. Took ages to get it right though.
Guess that goes to show that FD tuning is a bit of a black art rather than a science!
How much you can lower it before you get into the narrower part of the cage and rubbing issues will depend on a number of things – how high it is to start with, shape of cage (deores are wider than SLX – don’t have an XT to measure), wheelbase (shorter distance BB to rear axle = increased chain angle), size of largest sprocket on the back & chainwheel on the front (chain will run higher on larger diameter sprockets), and suspension travel on a FS bike (FD is fixed whilst cassette & thus chain moves up and down with suspension travel).
For example, I just measured my triple setup, and all I can say definitively is that for me and my setup the chain currently runs in the section of the cage that is 13mm wide, which is enough to use the whole range of the the cassette without chain rubbing on the FD cage. But, if I move the FD down by just 3mm the chain is now in a part of the cage that’s only 10mm wide, and no matter how much tweaking I do, it’ll rub at one end of the cassette or ‘tother. Now some people accept a little rubbing in 1 & 9 as normal, but I’m a bit anal about my gears and expect to use all 27 (or 18 in a double) without any annoying noises!
Can only suggest that the OP tries lowering his FD until he starts to get rubbing, and then he’ll know that’s as far as he should go with his setup.
I used a standard mech initially and found that the chain regularly dropped irrespective of how I tried to adjust it. An SLX double front mech fixed the problem immediately.
Surely if your chain didn’t drop when going between the middle and granny on your triple, then there’s no reason it should if you just take off the big ring. Unless … you changed something else in the process, like changed height of FD, chainline, or put on a different size middle ring – any of these things could introduce a new element that causes the chain to drop, and then the double FD with its different geometry would indeed be the solution.