I have played me and 2 friends (3v3) premade with 3 regs. I have to say it is broken at level 1, and only applifies into the late game. Essentially your opponents cannot lose any hp in there lane for fear of being triple sniped, which is 900 - 1500 damage every 15 seconds. When your in a room with each other it's very easy to do.
If 1 opponent doesn't stack health out of the gate (like an erubus doing minion build, or sedna / oak taking monks) you can literally ping them with a few auto attacks then tripple snipe for the kill. Lets not also forget the possibility of all 3 reguli taking heavens wrath. Thats a 2250 damage spike on command to any 1 target.
People say to counter, some things are way to cheese to counter, especially on certain maps. 3 Regulus on cataract can be a very difficulty battle. If you make a single mistake and they all get an assist on you, the game degrades really fast. Even regulus can stack HP, and when there whole team is getting 500 - 1000 gold every 30 or so seconds it will be GG.
I will write that even with 3 regulus on the field, there are viable ways to stop the game from being lost from the gates. Choosing characters with inherrently high stats, and then getting health items with a potion and a teleport can really turn the tides in your favor. Regulus has no interupt so teleports are his bane. Health pots for 275 can save you a 30 second death screen and prevent your enemies from gaining a 2k gold advantage. Getting +400 hp from the gates tends to have a better effect as you don't auto loose getting onto the field. BoTF is actually a good favor item for this purpose.
In the end though, only 1 teammate has to go a general with monks to ruin the game. In all other circumstances monks are the bread and butter of this game, but with 3 regulus your 1800 hp pool is going to be torn to shreads in under 3 seconds, and literally an assault from the crystal for an auto kill will have each regulus going onto the field with a second level and some much better gear than the opposition.