Remodeled our master bath. Bought a delta shower system. Double lever valve. One lever controls on/off the other lever in front controls hot and cold water. You would think putting the lever in the middle upright position would give warm water, it does not. I can only get burning hot. Or ice cold. First try we had not cold water or warm water, only hot. Changed the cold cartridge and now only hot or ice cold.
Maybe a back flow preventer is missing or defect. Normally, the cold water has higher (dynamic) pressure, since the hot water must flow through a heat exchanger somewhere near the heating system. And hot water tubes tend to have more residuals like lime stone coatings which decrease the throughput even more.
So as long as the cold water is flowing at the shower, it would press back any hot water. Result is cold water at the shower head. Only if the cold water is shut off, the hot water can reach to the shower head.
Many shower mixers have 2 BFP. And those BFP are prone to fail, they must be replaced after some years.