There are lots of them: https://quackr.io/ https://receive-smss.com/ https://sms24.me/ https://temp-number.com/ https://onlinesim.io/
They exist. Services treat control of the number as equivalent to control of the account, and expect you to maintain that control.
Throwaway phone numbers are not a viable low cost or no cost alternative in most normal user signup scenarios, and they're implemented as a privacy invasive form of spam prevention for that exact reason.
I use google voice, and in the past other virtual phone numbers but many services don’t fully work. When you request a code, you never receive it and in some cases they tell you they don’t accept the virtual number.
The numbers would quickly be blacklisted by websites. You need a very large pool of numbers and make sure you don't reuse numbers too often. Not sure if it's practical.
In the US, you can approximate this with a cheap prepaid service like a Tracfone.
Don't get it? Can you explain further ?
For about $20, you can buy a phone that comes with 10 minutes of talk time and has its own phone number. You can use that as a temp number. If you don't buy more time for that phone, the number will go away and you can then buy time for it and get a different number.
Or, what I do, is just keep it loaded with a minimal amount of minutes and use the same number for all such registration purposes.
I started doing this when I needed a whatsapp account, but didn't want to give facebook my phone number. I just keep that phone number alive, but never use it for anything else, and never even turn the phone on.
Sometimes won't work, especially larger sites.
I used to run a service that was using Twilio to do exactly what OP is asking. These sites often flag and block all phone numbers that are virtual or prepaid.
I've been doing this for about a decade and have never encountered that problem personally. Not saying that it doesn't happen, but it's uncommon enough for at least me to never come across it.
There are apps like Hushed where you can generate a working phone number for a pre-determined period of time.
I've always wondered what it would take to be my own telephone company and get an entire prefix, so I can give out unique phone numbers, kinda like how's privacy.com does for credit cards.