You're right. Addiction can happen with anything, it just may be less common with LSD or certain other substances. I have taken LSD and other tryptamines 100s of times and at times my intake patterns probably resembled an addiction.
Psychological addiction could form to anything pleasant, from peanut butter to MMORPG sessions. A real physiological addiction takes growing doses and a withdrawal syndrome. As far as I understand, LSD lacks both.
LSD absolutely requires increasing doses if you take it more than once every 1-2 weeks. When you take it daily, your tolerance sky rockets. There is also cross tolerance between LSD and other tryptamines/phenylethylamines.
There is a withdrawal in a different sense I think. I had HPPD for around 3 months after heavy psychedelic use with LSD as the centerpiece of that. I was doing up to 10 tabs at once and using mushrooms and certain research chemicals every two or three days for a few months.
Not to excuse my risky behavior, but other people go much harder than I do. MDMA is a favorite choice, especially in Europe where it is cheaper. There are endless stories on Erowid and Bluelight of young people buying 10 grams of a research chemical and plowing through it in a summer. Often it's stuff like MDPV or 25i NBOME, with a short history of human use and carrying cardiac risks.
A wide range of psychedelic drugs have addictive potential IMO. I'm not sure how meaningful the distinction really is between psychological and physiological in the context of addiction.
