I remember when I was 13 or so my parents sat my brothers and I down and asked us whether we continued wanting allowance for chores or if we preferred no allowance and they would simply buy us things we wanted periodically. We all opted for the former. We turned out fine (I think), but I personally believe it had more to do with our situation as a whole. My parents were in debt* up to the point where they considered filing bankruptcy (my dad worked in finance so they decided not to...would have impacted/threatened his job) so aside from the essentials (clothes and school) we were kinda forced to buy our own things. We all started working at 12 or 13 so that by the time we were 15 we could get a cheap ass car and pay for our own insurance/gas. I remember my grandma (who is well off) offered to buy each of us a car when we came of age, but my dad refused consistently, would always make sure birthday/christmas presents didnt exceed $100 in value, etc.
So yeah, it extends way past allowance imo. Even if, Allah willing, I am wealthy by the time I have kids I plan on treating them the same way.
*When we moved from LA to Hawaii, we kept our house in Northridge and rented it out. Got fugged up by the earthquake. Couldnt rent it after that. Foreclosure, etc.