Some years ago (decades by now), heat lamps were the default.
Brooder plates, and heating pads shaped into a cave-like space, are much more recent inventions.
My impression is that brooder plates are mostly used by people new to chickens (so no previous experience) and by people who did use heat lamps but then had a bad experience so they switched.
I think the people most likely to use heat lamps now are the ones who already have some experience with heat lamps, and who have not had problems.
Where you raise the chicks, and how many chicks, also make a big difference.
Heat lamps are good at providing large amounts of heat to a large area. This is good when raising large numbers of chicks, or raising chicks in cold conditions, or both. Brooder plates are good at providing smaller amounts of heat to a small area.
If a few chicks are in a plastic tub inside a human house, a heat lamp will easily overheat the chicks and kill them (or if it doesn't kill them, minor levels of overheating makes them more prone to some kinds of problems.) A brooder plate is a much better choice in that situation (or move the chicks to a bigger brooder, or use a smaller light bulb in the heat lamp.) That is a common situation with people new to chickens.
Obvious exceptions to all of that:
--chicks raised with a broody hen do not need any of those other heat sources.
--other heating methods may be good choices for any situation with very large numbers of chicks (over about 200). Those other methods can be ignored by most people with backyard flocks.