I think so, yes.
Evolutionarily, as humans, social inclusion was incredibly important. Being removed from a tribe was likely a death sentence. As such, we have some very strong social drivers like shame and embarrassment that people feel quite keenly.
But these social drivers caused people to do things that were good for society. You felt shame if you didn't contribute to hunting or gathering, cooking, planting and harvesting, building structures, raising children, or other crucial societal factors.
I think you're on pretty solid ground to say that shame and embarrassment go a long way toward the foundation of the society we have now.
I do think shame and embarrassment are useful tools that we shouldn't want to get rid of entirely. That being said, I think it's totally fair to question whether our current-society over-relies on these kinds of things, and asking if it would be healthier to scale them back rather than expand them.
You were probably thinking of completely different contexts.
Yes. Shame exists because it gave some evolutionary benefits to the primates who had it, like being able to live in a society and cooperate and don't cheat/kill/fuck over each other as much (if you think we do bad stuff too much, wait till you see what we can do without shame).
>I believe there are better ways to build relationships with others
The problem is that made-up (e.g. of our own making, requiring us to think about them and follow them rationally), not instinctual, ways, are none effective at all compared to innate, evolutionary, feelings like shame...
Well, with that I agree.
For one, it cheapens the quality and utility of shame.
Following this to the end, could end up with cheating on one's spouse or killing someone feeling only as bad as checking your Facebook page when you should be working...