Actually, there is a reason why. This description from a 2015 post by Tinman:
"The blast of cold water has to be stopped at the shower cold/hot valve. I am not talking about the on/off valve at shower head. Think about this! When you close the valve at the shower head the cold water has more pressure behind it that the hot water coming from the heater. That means cold water will push the hot water back into the tubing until both hot and cold pressure equalize... YOU NEED A CHECK VALVE AS CLOSE TO THE SHOWER VALVE AS POSSIBLE ON THE HOT WATER SIDE."
I saw a solution in Trailer Life that used a KES Shut Off Valve.
I installed it between the shower faucet and the hose to the shower handle. If it's more convenient, you can install the valve between the hose and the shower head itself. You simply use the new valve to turn off the water while soaping up then turn it back on to rinse. No more cold water blast.
Really simple and cheap. I ordered the part for $8 and installed it in about 3 minutes. It works great for the "Navy showers" required when dry camping and conserving fresh water.
Hope this helps your problem. Might be worth a try before changing out the W/H.