To have a combustion we need two things - light of high enough temperature and light of high enough energy concentration. The two are not the same. All visible light has high enough temperature. However the concentration is the problem
Why do we need high concentration for combustion? If we don't supply enough energy to compensate for heat loss, the area will never get hot enough.
By the way - interesting corollary of this is that even with sun lights - if we have a mechanism that takes away heat fast enough (say by blowing cold air at the area) we would not be able to reach combustion with large mirror in direct sunlight.
An interesting demonstration of this idea is putting a paper cup full of water into a fire. It won't burn where the water is touching it and eventually the water will start to boil.