We all deserve safe spaces, don't we? Of course. We'd go crazy without them. The ought to be safe spaces. Ought. "Ought" is one of those words that indicates that there aren't safe spaces. There are, in fact, unsafe spaces to be in. That's reality. That's a fact that we must face.
In general, the more public the space, the more uncontrolled the place, the less safe that space is. (With exceptions, of course.) In general, the more private the space, the more controlled the place, the more safe it is. (With exceptions, of course.)
The first questions is the biggie: Can we make all spaces safe for all people at all times? Ideally, the answer is yes, but practically, the answer is no. We cannot make a space safe for all people at all times. You can't do it. At best, we can make some space safe for some people at some times (or some combination thereof).
Our society makes limited safe spaces all the time. The restroom is the prime example, where a restroom is safe all of the time for either gender, but in practice, not really. A home is another safe space, thus having many laws tied to defending your own home. The space is safe, but not totally safe. The same is true of churches, clubs, tennis courts, parks, and doctor offices. Each is a safe space dedicated to a different type of space in support of a different purpose.
The current movement towards safe spaces is the US, in my mind, feels like a net being cast too wide. The purpose of these safe spaces is ill defined, too broad, too uncontrollable, and/or too unprotectable. Recall that each safe space can be made safe to its purpose, but going beyond that, such a safe place is not necessarily good to a different purpose. A church may be a safe place for religion, and a tennis court a safe place for tennis, but combining the two is bound to cause problems.
Consider for a moment making a University a safe place for all students, of all religions, and all nationalities, and gender identities, and sensitivities, and the professors who teach there, and you wind up with a significantly broad mandate, one which is impossible to meet. Through history, universities have made safe space, but ones focuses on gender (female dorms), interests (clubs), academics (classrooms), and so on. The idea of overarching safety was one shared by society as a whole, a freedom from assault and violence. Beyond that, no reasonable institution would attempt as a universal safe space because that sort of space was impossible to design and manage. The results would have either been laughably inadequate or unlaughably oppressive.
The question then comes, what of the ideal? Should we simply skip the ideal because it's hard? Of course not. I think that the idea is always one worth pushing, but as the problem doesn't exist in a vacuum, it can't be solved in a vacuum. Safe spaces is a problem that exists within the society and can only be addressed within society, one where there are competing interests that have the same "ought to" mandate of safe spaces. Which priority wins? That's up for us to decide. There's no answer in the back of a book. The solution that we come up with today can easily become the distastefuls of tomorrow. Indeed, every generation or two, these questions get re-asked and the calculus resolved, the downsides re-explored, and the solution, eventually, found distasteful.
Even among safe spaces, not all are equal. Some safe spaces require higher priority than other safe spaces. Not all needs can be made equal, not by desire, nor by majority, nor by merit. We are left with an uncomfortable hierarchy of importance, one that is determined by us, so the importance can change.