33Mail doesn't just give you an email alias, it gives you an email domain under which you can create as many aliases as you need.
These aliases will instantly forward to your main email address, and you can even reply to them anonymously without revealing your real address.
The aliases aren't time-limited, so you can use them with any website - only deleting them if the website starts to send you email you don't want.
There is a generous free tier, but for $1/month you can upgrade so that you can use your own domain name, along with various other benefits.
33Mail has been around since 2011, so it's not a "here today, gone tomorrow" startup.