When the previous owner vacated the premisis he painted the whole house in
cheap white paint. I've since noticed that the paint under the kitchen sink
light is badly cracked and peeling. I can only presume it's from the
exposed light bulb that is probably an inch from the ceiling. My concern is
whether or not the peeling and cracking is from having a light bulb too
close to the ceiling (it's a standard 60 Watt bulb) or from other reasons.

The only other reasons I can think of are
1) He turned the light on too soon after painting and the wet paint cracked
and peeled from uneven drying
2) The paint is super cheap and that's just what super cheap paint does

So really my question is, should I go ahead and paint the ceiling in my
kitchen will I have to face this problem if I use a good quality latex? The
fixture itself is gone, it looks horrifyingly ugly anyway but that doesn't
mean the replacement won't be just as close to the ceiling.