Should NCOs inspect barracks during the weekend?

US military have rules to follow, and those rules are enforced.

Never needed to.
Barracks were squared away.
Policed each other.

The Timing and attitude of the leadership who are doing the check up makes the difference. Have the NCO just quickly do a common area walk thru and unless there is a safety risk don't make any corrections or knock on any doors to gather up soldiers to correct a issue. Just make not of it, if you can take a picture without being seen than do so and handle this on Monday. Room ispections need not be happening on the weekend. But bottom line barracks inspections have time and time proven that they are necessary. As a Soldier who lived in the barracks into the rank of SSG, soldiers maintain the barracks far differently than housing. Always have.

Sounds to me like the army has another self inflicted problem. I wonder how Patton would handle it.

If the living conditions in the barracks have gotten to the point where it was determined that daily inspections were warranted then yes do what needs to be done to ensure a healthy living environment. With regards to those talking about people living in military housing or off post, before retiring we did do health and welfare inspections at military housing when it was determined necessary. If a Soldier living off post in a shady part of town we would check them too. Generally with regard to military and off post housing we gave a 24 hour notice we were coming over. If the home was not trashed out then there wasn't any issues. If it was trashed they were told they had x amount of time to get it fixed and we would be back. If it continued the Soldier was ordered to move into the barracks until the CoC determined they could live in housing within the standards required to maintain a healthy living environment.

Good leadership means developing trust and respect within your scope of responsibility. That should include periodic visits to barracks and married housing. Well announced on a mutual respect for privacy. (unless there is reported or suspect criminal activity. Then Security Police or Commanders.)
But daily is too extreme and indicates to the troops that they are not trusted and is treating them like children. If we trust them with thousands and sometimes millions of dollars of military hardware then they should be trusted to unobtrusive barracks life.
This indicates to me a failure of leadership at the supervisors level including commanders.

Exactly but to all who think you can't inspect quarters check the regs, because unless it's changed since I retired you damn sure can. Civilians may not be accountable but their soldier is. I used to do all the time if it was warranted. Read my comments you'll see.

For one that goes against everything BOSS was created for. Daily is definitely a terrible idea. Soldiers are going to think WTH and definitely going to destroy morale. Definitely intrusive. If I was still in I would go to1SG and convince them that if we have to do barracks soldiers than we need to do family housing as well. See how long it lasts when Everyone has to do it including CO's and 1SG's have to be inspected too. O guess the military is going backwards on everything. Yes to discipline again but hell no to interrupting people's lives. If you absolutely have to it should be quick and non invasive as possible. The inspections should be on duty time not soldiers personal time and definitely not at 0 dark thirty either. Skiers in barracks deserve the same courtesy that married soldiers are allowed. And don't say you can't Inspect quarters because unless the Regs have changed you damn sure can. I had an NCO that I got rumors about I went to his quarters and did a health and welfare and his family was living dirty. I gave him one week to clean it or I was going g to have his family shipped home and move him into the barracks.

I am from the open squad bay and using wall lockers for blocking to get some degree of privacy.
A time when the Company Gunny checked the barracks daily, the Company Shirt checked after weekly field day and the Duty walked through on weekends.
What has happened to the concept that leadership includes caring about well being as well?

No it is not intrusive! It is a health and welfare issue.
While pulling duty as the BN and BDE SDO. I was to walk through the barracks during my duty rounds. I cannot tell you how many times I walked through a company and found that their latrines had plugged toilets or that someone had puked all over the showers.
I always took the same action; council the CQ and ensure that those deficiencies were corrected.