(The claimed rationale for limiting the number of taxis is to reduce traffic. I would suspect the actual rationale is to favor the existing taxi businesses that already have licenses and don't want competition.)
Not that this is any better, but people talk as if there's One Way taxi regulations work all over and there's quite a wide range on these things.
Also, the nominal reason for limiting plates is usually (as far as I've ever seen) to ensure a living wage for taxi drivers. I don't think it really works out that way, instead creating a class system where some people extract rent from other people.
When Uber started operating in Quebec the price of a plate in Montreal dropper to around 160K. That was the major point of dispute, since taxi drivers usually get loans to buy these plates knowing that they can re-sell then anytime. Uber changed that.
So fundamentally their complaint is: "My investment carried a risk"
The ratio of vehicles per person in Singapore is 0.18 (compare to about ~0.5 most places in the US). It's very easy to get a Taxi to any place not accessible by public transport. I would be astounded if there is any verifiable scientific study backing this claim.
[0] https://www.lta.gov.sg/content/dam/ltaweb/corp/PublicationsR... [1] https://en.wikipedia.org/wiki/List_of_U.S._states_by_vehicle...
If you're in the downtown area anytime close to rush hour it's practically impossible to get a cab without reserving one in advance (which costs extra), or waiting in line at a designated "taxi stand" for an unacceptably long time.
Personally I think that part of the reason the government no longer allows street hails downtown (even for cabs) is an acknowledgment of this problem.