A short focal length/high magnification lens has the slight advantage that it needs to be closer to the tinder.
In most circumstances it is easier to hold the lens steady and at a short distance than at a longer distance.
The actual light gathered is indeed in proportion to the area and not the magnification.

I have started fires in very marginal conditions by use of a large Fresnel lens, the smaller credit card sized ones only work reliably in ideal conditions IME.

As has already been posted, a fire is most needed in conditions when a lens is useless. Still worth carrying though IMHO, each fire started thus is one more match left for less favourable conditions.

A large Fresnel lens, say A4 sized will start fires in unfavourable conditions and is worth stocking in a long term TEOTWAWKI kit, but is unlikely to worth carry in a backpack.

In good sunlight an A4 Fresnel lens will light a fire of large sticks without any need to procure tinder.