Rank has its privileges means what precisely?

I understand that higher rank has more latitude and is empowered to serve the mission as they see fit without direct supervision. STILL follow regs and if anything, despite having more latitude your decisions are under more scrutiny

No special privileges WRT violating policy or law. Unless you're a COL or above there are few perks either. Maybe a reserved parking space at BN CP or similar, but the burden of Command far outweighs things like this. Even writing fitness reports at a Platoon or Company level can be a formidable task, if you appraise accurately and fairly. Luckily, the reporting periods are spread across the calendar for different ranks. I often had 8-10 Sgts, 5-6 SSgts, a Gunny or two and at least one, maybe two MSgts or one MGySgt to report on. The reports are no joke either, because you hold the future of these Marines and the Corps in your hand. Besides that, you have requirements for periodic and documented counselling so there are no surprises when they sign their report. This is just a small slice of the responsibilities of BN COs or higher. I found in research recently that the new USMC fitness report form is 6 pages long as opposed to the double-sided one page report of the past. It's just one example, but added to the daily administration of training, organizing, and equipping your unit for deployment, it all adds up. If anything, the higher the rank, the greater the responsibility. If you take your job seriously that is.

I've always used it more as a punch line than taken it literally. Yes the higher you go the more perks you get, hence the saying. That does not mean that those privileges are there to be abused - though some may do so. I first used that phrase when I took company command and got my own office. I used to call people in just so I could throw them out, citing RHIP. If anything my rank gave me the privilege of commanding some fine troops.

Side note what I hate is when the spouse wears their rank then you will see some time how bad it is
One day my unit go called in and I stop to pick up some donuts for my guys. And there was a E
One star Generals wife Trying to push her way to the front of the line I was just about to get my order and she Reyes to push her way past me. I stayed “Excuse me” and she Said “I am General so and so wife let me by” and I replied with “Do You know who I am?” And she said “No” so I said “Good by” and walked out with my order
It is all part of life. Just remember not to be a Jerk when you get the rank

Exactly the opposite! While rank does have privileges, violation of rules, policies, regulation or law is NOT one of them. In fact, good leaders set the example. A story from long ago and far away. I was XO of an admin company and lived about 35 miles away. This is back when alarm clocks ran on plug-power and we had a power outage overnight. When my alarm went off it was about an hour after when it should have. I called the company office to speak to the CO but he wasn't aboard yet. I asked the Duty NCO to pass the word to the CO that I would be about 35 minutes "late." When I arrived, the 1st Sgt was storming around the duty desk with smoke coming out of his ears! It took a while to calm him down enough for him to show me the Duty NCO Log entry that fired him off. It read, "0720, Capt Carlson (XO) called and stated a power outage at his quarters overnight meant he would be about 35 minutes late. He asked that I advise the CO. I granted the normal 24-hour extension of liberty." Meanwhile the 1st Sgt kept muttering, "He never should have made an entry about an officer, certainly not the XO." I said to him, "OK, 1st Sgt, the 24-hour extension comment is a bit tongue-in-cheek, but here's my take on this. I'm glad it's there in the Duty NCO Log. You and I both know that every junior Marine who stands Assistant Duty NCO has nothing to do from about 0100 to 0500 so they read the log book to stay awake. That entry says two things that are really important. First, it says that liberty regulations apply to everyone in this company from the CO and XO on down. Second, it says that when Maj Hicks (the CO) says that if anyone calls in before liberty expires, the Duty NCO has full authority from him to grant a 24-hour extension, no questions asked, he means it -- even when it's the XO calling in." The 1st Sgt said he was just concerned that it was embarrassing for an officer to be noted that way in the log book. I replied that not only was I NOT embarrassed, I was happy to have an entry that said I was just as much bound by regulation and policy as any other Marine in the company.

Rank does have its privileges but I found it comes at a very high cost,my LT in Vietnam was a fine example of this because of his leadership and professionalism in the field, this was sorely missed after his six month field tour ended,his replacements were capable but not outstanding ,as for a non combat situations most of the officers I served under had their own agenda some good some bad,that I think you could apply to most circumstances .