Is there any benefit for turning off the ability to train certain skills when doing combat?

If you are creating what is known as a "Pure" account, then it has advantages. For example, a "Strength" pure will only train Strength as a combat skill, and will aim to leave every other combat skill at 1. Being able to turn off earning experience for certain skills will prevent them from accidentally leveling those skills and "ruining" their Pure account. It will also allow them to do things like cast basic spells or use ranged attacks for certain scenarios without fear of leveling them.

In addition to the other answer, training multiple skills at once will spread the XP earned across the selected skills evenly (something the other answer didn't address):

Players can change which combat skills receive experience via Combat Settings, in the Powers interface. Experience earned with each combat class can be put toward its related skills, or to Defence, or split between them.

This effectively makes it slower to train individual skills when you have multiple skills selected, however it will keep the skill levels even (so long as they start at around the same point of experience).

Runescape has always been this way. In the past, when using melee, you would have the ability to select between different attack types, something like this:

Attack types

Depending on which one you had selected, a different skill was trained (In this example, Chop would be Attack, Slash would be Strength, Lunge would be shared between Attack and Strength, and Block would be for Defence).

With Magic, you could cast spells defensively if you used a staff which would grant Magic and Defence experience, and using the Long Range option when ranging would grant both Range and Defence experience. Now with the new system, they made it more clear on what skill you want to train.

In addition to the other answers, I was curious if there was a way to increase XP going to Constitution

Testing with Magic combat, I tested toggling gaining Magic/Defence XP and killing 10 white wolves (200 health) each

Note that the only options are Magic and Defence, Magic only, and Defense only, they can't both be disabled

      |Both| Mag| Def
Mag XP| 150| 300|   0
Def XP| 300|   0| 600
Con XP|  99|  99|  99

So it looks like Constitution XP does not depend on XP settings and that Defence XP is twice as easy to get as Magic XP