I think, you need to look at this in the context of cultural norms, which, I suspect, might be different in Sweden where you live and here, in the US.

Here, if you don't show up at your scheduled therapy session, you, in most cases, will be charged the full fee for the session. The same will happen if you cancel late. Most therapist, just like medical doctors, have a 24 or 48 hrs cancellation policy. If you don't cancel within this window of time, you'll be paying the full service fee. This is the situation in private practices. In most agencies, people also pay for services out of pocket. There are few places where people can get MH services free of charge. You have to be eligible for that and, oftentimes, those services do not resemble traditional talk therapy.

As you see, in this context, the therapist or the agency they work for would have to contact you after your no show just to retrieve the payment for the missed session, if not for any other reason. So, that's why here it'd be unusual for a therapist not to call a client who didn't show up.

In Sweden, as I've heard, many people can get psychotherapy free of charge because many professionals work for the state agencies, the are salaried employees so they don't do fee-for-service work. I don't know if this is your case or not. I think, if a therapist works for a salary and it makes no difference to them financially whether the client comes or not, then the expectations of appropriate or "normal" professional behavior might be different. I think, some therapists would still choose to call the client ( I personally would) but some wouldn't and that might not be considered an uncaring behavior. This might be perceived as a sign of respect for the client's choice.

So, I don't know what kind of settings your therapist works for and what are the general cultural norms of behavior for therapist in your country vs the US or any other place. By the way, "cultural" norms are not necessarily the same as "ethical" norms. Those two are not interchangeable.

Speaking generally, I don't know if I'd come back to see the therapist who didn't call me to check on me. It depends on many other things that were happening in therapy, so that would not be necessarily my "ultimate test" of the therapist's caring. But that might make me to pause and to reflect on what I need from a therapist. If this doesn't fit into my idea of a caring attitude given the entire context of my therapy, then yeah, I might not go back. But, as others said, this would not be just one single factor for me.