You guessed right -- mirrors are expensive, and also heavy; plus it's yet another piece to align (in infrared, so you can't use unaided vision to align the optics; yes, you can use a coaxial visible beam to help with this but that's also expensive and hard for various reasons). If you're using an incoherent light source there's also the problem of collecting all that light and focusing it onto the sample, and each optical element incurs some loss of light.
In the end, the actual LEDs themselves are tiny; a PCB containing the LEDs + driver ICs is smaller, lighter, and brighter than any mirror/lens assembly I could easily source with the requisite coatings to operate efficiently in this frequency band.
For a laser source, a fiber optic source can make a lot of sense, but fiber optics optimized for this frequency of light turn out to be pretty expensive, and the termination of the fiber optic still needs a collimator lens. At the end of the day, the net weight and cost budget still works out in favor of mounting a laser diode directly on the microscope head, so long as the power requirement is under a watt. Beyond that, the weight of the heat sink starts to be a factor, and an off-board laser starts to make more sense.