Should septic tanks be cleaned on a regular schedule (every 3 years)?

Not necessarily. If everything is moving through the lines easily, there's no need to clean it out. I have 2 that's 20 years old, never been cleaned out and work fine.

Most well-designed systems have enough space for 3-5 years of use. It's recommended that septic tanks get pumped every three years.

"If it ain't broke, don't fix it."

If it's working without backing up I don't think it needs cleaning but you could feed it some yeast to boost the good bacteria that makes it work. I just flush a package of dry yeast {open pack and pour the yeast in toilet, not unopened package) down it once a year. If your tank needs it great, if it doesn't it won't hurt it.

NO, it does not have to be cleaned every three years. That's an average. It depends upon various things: How the tank is sized, how many people use it, what is put down there, ie: like food and grease from a sink grinder. You can ask how much it would cost just to have someone come check to see if it needs pumping. I have one and only put toilet paper specially made for septic tanks. Nothing else goes in it!