Figure 2: Modern vs older bike drop comparison.
What happens when a cyclist has limited mobility and a very aggressive geometry (lots of reach and drop), they end up riding with a rounded lower back (Fig., 1). This can place the lower back under extra load which can cause pain, discomfort and potentially injury. Beyond the back pain, it can also have a knock-on effect causing saddle discomfort.
While not every case of lower back pain is caused by poor mobility, improving it can sometimes help.
If you are very tight/stiff, doing some dynamic stretches may aid comfort for the upcoming ride. This along with a good warm up on the bike is good preparation before hard efforts. It is important to avoid static stretches before the ride as this will negatively affect performance.
While the temptation after the ride is to head straight to the fridge and then the couch/chair, stretching after your ride for 5-10 minutes can help maintain or improve your mobility. It is best to stretch when the muscles are warm. This is best done after exercise but can also be done after a warm bath or shower.
Not everyone needs to stretch. Some individuals who have good mobility, may simply need to maintain rather than improve. For those who have poor mobility, improving this with regular stretching may help avoid discomfort on the bike. For some, the equation is simple. Stretch to get more comfortable.
Another note is when considering your bike setup, it is worth factoring in your mobility.