Is the Army too rigid when it comes to friendship with higher/lower service members?

The fraternization policies are there for a reason. There's nothing wrong with being friendly with people of different ranks, but when you form friendships outside of work it can affect your work relationship.

Say you have a SPC who is a friend of his SFC platoon sergeant. Even if that SPC is high speed and deserves to go to the board, other soldiers may think it is favoritism if he is sent. If the SPC happens to mention an issue he is having to the SFC it could also put a strain on relationships with the team or squad leader if they feel the SPC is circumventing the chain of command.

The best way to avoid this is make sure it is an open invitation whenever you do anything outside of work. As a leader you can have a BBQ at your house and invite soldiers, but you need to make sure you invite all the soldiers and not just the ones you like. You also have to make sure that you act professional even if it is off work (no getting drunk or allowing people to drive drunk).

I never had that issue. I seemed to get along with very few of the seniors even when I became one. I was never a good staffer. I was always in the trenches and all that mattered to me was keeping the birds in the air. I was a workaholic and workaholics find other workaholics. Life was a lot different back then. When I got home it was kids time. Me time was the rifle range and my daughter was my sidekick.