The short answer is "yes" but it's nothing but easy.

SaaS or paying versions (whether the extra features are open source or not) are possible financing sources.

However SaaS requires specific investments which don't finance the open source software itself and you need to factor them in.

As you say, people can self host so you have a "competitor" for your offering. One way to handle this is to have the same free tier in your SaaS than in your self hosting and you can provide paying versions also on the self hosting. Note that you can do paying version that is open source. At XWiki (xwiki.org xwiki.com) we do this with our Apps Store and paying extensions, but all our extensions are Open Source but not deployed for free. This shows our commitment to Open Source. We show to the community that we need ways to pay, but we also show that we are not trying to close down the projection or refuse collaboration and competition with our community.

You could also not have a free tier or smaller tier on SaaS and concentrate on the easy of getting the full service running and ready to go. Now a significant part of open source users are here for the self hosting and keep control. Others are also in for getting things for free (either because they like free, or their boss likes free, or even because buying is complicated). But these free users are also your marketing. Never forget that when you try to get some revenue. It's easy to turn back on your community. In the end you need the free users to prove the project and if you make all paying the reach is reduced. From my pov, the goal is to create more Open Source, not more revenue. The revenue is there to make more Open Source.

So in the end, the paying users will always be a small percentage of you free users. It can be 1% percent. Could be more or less depending on the type of users or software. On SaaS with individuals same rules as free tier that's not open source can apply and be even less.

Now the key is also to have great software. More happy free users, more paying ones.. Same for donations.

But if you start asking for money, whichever method, it's good to be transparent about it. How much money is made, how.. What do you do for it. For example in one comment, somebody mentioned donations going down when launching a service. This can easily happen as users have not idea what's going behind the scenes, because they don't have the numbers. For cryptpad (cryptpad.org) we decided we should publish the numbers. It's not easy to keep it up to date as we work a lot to build the software, developer offers, find funding from projects and so on. But we try. See an example here:
https://blog.cryptpad.org/2023/02/09/CryptPad-Funding-Status...

On the XWiki side, we would want to do it too, but lack time, and most of our funders are not companies, which are more interested on how competitive our offer is towards proprietary solutions, than how we fund it. This is also key in the end. Companies and Users have money. They just use it for what they really need and for that they will very often look for the best offer. As opensourcer you still have to convince that it's the best offer and most users won't really care about the fact that it's open source. We still have to convince them that Open Source is valuable in itself and that users should actually pay more for it..

Hope this helps..
Ludovic, XWiki and CryptPad