Breathing accomplishes two things. It gets rid of carbon dioxide waste and it takes in oxygen needed for fueling. The rate of breathing whether at rest or while exercising is a balance of these two needs. A build up of carbon dioxide is usually the driver of the urgent feeling needing a breath.
Swimming is no different...your breathing should be dictated by your needs, not by your skill, will or philosophy of what breathing pattern is best.
At relaxed warmup speeds, you may only need to breath every 4, 5, 6 or even 7 strokes due to low muscle activation, low production of carbon dioxide and a low utilization of the oxygen already dissolved in your blood stream and bound to your red blood cells.
As your effort increases, your need to breath increases in frequency. At some level of exerition, breathing every 3 strokes will be the ideal "match" for your needs to exchange air. If you can't do it because you have only taught yourself to breath on one side, you're forced to either a) slow down or b) breath every 2 strokes which can leave you feeling rushed and lightheaded or c) breath every 4 strokes which will definitely leave you feeling breathless since you begin retaining CO2 in your blood.
If you can breathe to either side at will, and have practiced an every 3 breathing pattern, then you can swim right at that level which is matched by breaths every 3 strokes. This is the value of bilateral breathing...when you swim at a level that requires a breath every 3 strokes. But if you don't practice it, when you need it, it will feel far less comfortable.
When I have had those few wonderful moments when my breathing technique is relaxed and dialed in, my pattern is executed without thinking and the frequency of breaths matched with my exertion level...it feels like I can literally breath underwater. it's the coolest swim feeling I've ever had and is extremely elusive for me