There are online services that get you a single use phone number for a couple cents (depending on the service – Instagram is 30–50 cents for example). I use SMS-REG but I'm not happy with it lately (many times SMS just doesn't go through; and credit refilling is tedious).
Won't help with friends uploading your number to WhatsApp though.
I very explicitly stated "a single secondary number doesn't work" so this is the exact sort of thing that is not a solution to this problem.
There are a million services that give you a single additional phone number, but AFAIK none that let you generate any number of completely anonymous virtual numbers that forward to your real number, like what privacy.com does. (I think there are a bunch that let you buy each additional phone number and have them each contain their own inbox and everything, but none of them really act as just free relay services like what privacy.com does.)
privacy.com also locks each number to a single merchant, allows me to instantly revoke numbers that have been compromised or that are no longer going to be used, allows me to get credit for fraudulent purchases without having to file a real chargeback (I do realize this doesn't really have a phone-number equivalent, but you get the idea), etc. absolutely invaluable protection layer.
Yeah, this is not a single additional number though – they give you a new random number for like 5 minutes which is enough to set up the account but obviously not enough to use it afterwards. I guess they do it so that they can allow reusing the number with other services.
Why there's no service generating multiple permanent virtual numbers is a mystery to me, too. They don't seem much more scarce than credit card numbers. On the other hand, only Privacy.com seems to allow issuing that many cards (in contrast, Revolut only allows you to have 5 permanent cards + 1 single use card – this seems to be the usual limit in other banks as well), so they might know some kind of a secret sauce.
privacy.com does have a secret sauce - a direct partnership with Visa that allows them to register cards that don't show up as "pre-paid". As far as I know, nobody else has this. I don't remember what they used before - perhaps still Visa, just pre-paid.
I don't think there is any major residential phone provider that would offer that sort of partnership to the point where you could trick services like OpenAI into thinking that the number is that of a real person. Aaand spinning up any new phone provider for this purpose is like registering a brand new super-blockable ASN for a VPN's IP addresses.
FWIW, Telnyx allows you to keep phone numbers indefinitely, and receive/forward SMS messages and phone calls. But they do not offer an integration out of the box - you'd have to code that up yourself using their APIs. And each phone number you allocate has to be paid for individually. And also, Telnyx is super detactable and blockable, of course.
Slightly tangential but I'm wondering how hard would it be to build a “bring your own eSIM” kind of service that you can register an external SIM profile QR code with and it would host it with a SIP interface for voice + some kind of API for SMS, and allow you to switch active line between different SIM profiles on the go. (Charge something like 10 ¢/mo per profile stored, and $5/mo per active line?)
Won't help with friends uploading your number to WhatsApp though.