I have various keyed chucks, Jacobs, Rohm, No-Name and they all work. I have two keyless chucks, both economy models. The one on a portable drill is completely useless, a bigger one I bought as a stand alone needs a gorilla-style grip to tighten. I fitted it to an MT2 shank and keep a centre drill in it.
The lesson, if you buy budget, buy keyed chucks. I’m sure teh more expensive keyless ones are OK, but I have never bought one.
Neil