You’re correct in that you should use whatever sling works for you, and if you’re still using that old M60  sling set-up that you used to use “back in the day” works for you, great. Sling technology and technique has come along way since then though. Single point, two point, and triple point slings are now available that make it generally better to use the sling than the archaic idea of “no slings on patrol”. There’s too many out there to bother naming, and all have strengths and weaknesses, but when sling shopping, look for a sling that does what you want it to do. For you, the M60 sling does what you want, that’s fine. I prefer a sling that keeps the gun in a specific position and orientation for transitions to my sidearm, and for other things like operating equipment, driving, opening doors and admin use, but still keeps the rifle exactly in
the same spot, with the same side against my body, and does so comfortably. Of the slings out there, most are a variation on the theme. Single point slings attach the rifle to you at one point on the weapon. This arrangement can be anything from a loop, to a snap link [rock climbing carabiner] running through the stock of your M4  and attached to your body armor, to far more complicated stuff.
Two point slings, like the M60 you use, or the Israeli, and most other “tactical slings” are like this. I use the Israeli sling and it’s a good, effective and simple device. The sling is a very long strap. The strap is adjustable, and there’s also a Fastex-type buckle that you use to shorten it a specific amount. The slack when the buckle is connected is equipped with velcro and stays secure and out of the way. This way the rifle can be slung over your head and shoulder, more comfortably and more securely, but the
simple release of the Fastex buckle will allow you the extra length needed to use the rifle with no problems. It has both hooks and para cord for attachment. There is a compartment that you can keep earplugs in. The Israeli sling does everything fairly well, and some things quite well, though it’s slower to employ in some cases. As an all-purpose, general use sling for doing other things while remaining armed and able to fight quickly, it’s one of the best I’ve run across. Not what I prefer to use if I know I’m going to fight, but it’s what I prefer to use if I just need to have a long gun with me.
Other tactical slings get more complicated in use, but are better for fighting than the Israeli sling. These slings seem to most novices and many old-timers;) as contraptions that you don’t need, but properly employed are quite useful. The British SA-80  sling is slightly over-complicated for what it does, but it and most other tactical slings work all abut the same. Some are just simpler to figure out. Some guns, like the older HK  roller-delayed based line, actually have a third mounting point for special sling. If you have a weapon so equipped, then full advantage should be taken.
Which sling is the right one for you to use is a matter of what you want that sling to do for you. The Israeli sling is pretty hard to beat for most general use though. I’d take it over most of the “tactical” slings for everyday use in 95% of the situations you’d encounter in real life. If you have to lug a rifle around with you and still live your life, it’s just the ticket. Which is why the Israelis designed it that way. – “Doug Carlton”
JWR: Adds: Some of you that have read my novel “Patriots ” may recognize “Doug Carlton.” Like a lot of the other characters in the book, “Doug” was based on a real-life friend of mine, that I’ve known since college. We went through ROTC  together. “Doug” later went on to be a distinguished U.S. Army helicopter pilot. He now works in the transportation industry on the East Coast.