As an old roadie cyclist and former cycling advocate (working in NYC educating motorists about sharing the road with bikes and working with the city government to promote cycling and removing barriers to same), I was very dismayed when Cozumel chose to segregate bikes from the main traffic flow. The decision was in reaction to a problem that required a totally different solution.
Usually, the first move of government is to establish a bicycle corridor. The second is to prohibit cyclists from using the primary traffic corridor when a bicycle path or lane is available. The fact that #2 didn't happen is both a good and bad thing. The bicycle road is under utilized and motorists are very much inconvenienced. On the good side, the city is complying with the State motor vehicle code, which lists bicycles as vehicles with all rights and privileges to use local roads, hence no regulation limiting cycling to the old road.
That bicycles are vehicles is the point to remember. Cyclists have rights to occupy a traffic lane same as the drivers of cars. They may ride two or three abreast in traffic. They should not operate their vehicles on the shoulder, which is dangerous positioning, unless it is safe and it is as a courtesy to the operators of other vehicles.
If I had a say, which I don't, I would recommend that the city return the old road to its former use and educate residents about sharing all roads with all of the different vehicles that are found here. It's a lovely piece of paradise for the enjoyment of all!