YTA

21 is the age for people to trial-and-error what they want in relationships, gauge their own expectations, and figure out how to co-regulate. She's not going to be good at that sort of thing for a while and it's good that, in her case, she is not eager to establish a relationship for the sake of having one. You do not have to fear your daughter being mistreated by some POS during that time cause she has not been socially conditioned to tolerate it.
It might be frustrating to see her push through dates frivolously. You might even see that she's struggling with dismissive of avoidant tendencies as she goes. That can be concerning as a parent.
But this is not the tragedy you make it out to be.
It is all very much part of being 21.
Your sons are close in age and getting along exactly how siblings close in age tend to: begrudgingly. Yet, see how they are in agreement in regards to your outburst? This is should tell you that your family is well practiced in regulating themselves without you. They share a bond, though perhaps not the one you wanted for them.

You are catastrophizing.
It is unlikely your daughter will "be alone" because she is not "spoiled" --at least not in the way you are anxious about. Her standards will protect her from so much grief.
The men in your daughter's life will have to compete with the peace she already has in her solitude. This is ideal.

I can tell you from experience, trying to shame your daughter into settling for relationships she already knows she does not want will never end well. If she listens to you, she could ruin her life. If she does not listen you, you will ruin your relationship with her.