What is the advantage of the lobster design over just plain mitts?

The "claw" helps with shifting and braking dexterity vs mittens.

Thanks, I can see fine braking touch.

I finally found gloves I can use after years of searching. I have a huge pile of gloves that work up to a point and then my hands get cold. These Gordini mittens are paper thin, and I thought, these can't possibly work. And they do. They are so thin, I can pick up a quarter. Plus they have that inductance-passing feature that I can use a smartphone with the mittens on! When it gets very cold, I put these cheap gloves on under the mittens, and that works. I rarely need to. I rode over an hour each way yesterday without the gloves. My hands get cool but not cold. The mittens have so much room that I can make a fist when it's safe to do so, and that warms my hand back up.

Just a note: If you wear ski mittens, make sure you turn them inside out to dry, in between rides. Wet, sweaty mitts can get pretty funky, and also lose their ability to insulate.

I like the Kinco insulated hi-vis work gloves down to 18F and are a good value at $15 or so.

and the skiing lobster claw mittens are good to about 0F, and much more spendy.

The loose index finger works very well with rapidfire shifters.

Since I have a dedicated winter bike with 1x gearing, I chose a shift lever that's easy to work with fairly thick mittens. This arrangement has worked for temps pushing -10 F so far. And for Xmas I got a pair of bar mitts, which are really nice.

A grip shifter should have worked for this purpose, but it was aggravating my tennis elbow.

I have had issues with my fingers no matter what gloves I have tried. It seems that I have some issue with circulation. This year I purchased these:

Heated Gloves - Bay Cycle And Sports - Pickering, Ontario, Canada

I use them like a liner inside heavier gloves. I am really happy with them. I have been out in sub freezing temps and my hands have remained comfortable.