Warrant rank goes back at least to the Royal Navy, where sailing masters, gunners and other specialists were given warrants. This gave them certain privileges and better pay than ordinary sailors. The actual way the ranks were used varied widely over the years.
I was in the Army in the 60s, so my information is a bit dated, although the Army warrant system hasn‘t changed much except for the addition of one more step (CWO-5).
The Army was like other branches in that certain specialists were given warrants so they could enjoy some of the prerequisites of officer rank and pay. It was better to retire as a warrant than as a master sergeant -- the pay was higher.
The Navy and Marines use warrant rank, although in a different manner than the Army.
Up until WW2 there were only seven enlisted ranks, private through master sergeant. Thus, senior enlisted personnel with valuable technical skills were limited in how far they could go, both in prestige and pay. Warrant rank rewarded those soldiers for their service and skills.
The twist came about when the Army decided that it was a hassle to have all officers flying aircraft. Remember, during the Vietnam war the Army had more pilots and planes than the Air Force. I‘m not trying to denigrate the flyboys here, but each helo required two pilots, just like a B-52. And the Army had lots of them.
An officer may have technical skills, but an officer‘s overall objective is supposedly to pursue a military career designed to fit them for unit command. Thus, professional education and requirements tend to collide with the need for training and practice in technical skills. This is not a problem for warrants. Their objective is to be skilled aviators or whatever.
My personal opinion is that a good deal of the flying done by all services would be better handled by warrants. Many nations, including the US, have had very capable pilots who began their careers as enlisted pilots, for goodness sake. From the perspective of responsibility -- the US Army routinely assigns sergeants to command battle tanks, with far more destructive power than most aircraft.
Warrant officers, when I was in, were referred to as "Mr." or "Ma‘am", and the rule was that you saluted a warrant the first time you met during the day. That was stupid. My unit had about forty warrants assigned (CH-47A company). How was I to remember who I had saluted? We highballed ‘em all, every time, although in VN many of the rules were relaxed at the unit level because we had too many other things going on to drop our tasks and come to attention every time an officer entered a room.
Hope some of this helps. Major Baker might be able to add to this info. Some of the details have changed since I was a pup.
Jim