Why do some LEDs light VERY slowly when power is applied?
Bare LEDs are generally quite fast.  The ones with phosphor to re-emit a different color are slower.  How much slower depends on the phosphor.  White LEDs, for example, have phosphors.  Those would be silly in a opto-isolator.

Commercial opto-isolators use infrared LEDs, usually in the 9xx nm wavelength.

Look at the current spec for commercial opto-isolators.  Note that they require significantly more than 10 &micro;A of input current to work.  What a LED does with only 10 &micro;A is irrelevant to opto-coupler use since they aren't being run at such low currents.  Usually a few mA is expected.