You are confusing different classes. The lightest self-propelled towed gun in the world today is the Israeli ATHOS and it weighs 12-13 tons.
AH4's equivalent is M777 or the Indian MAG-ER (8 tons steel) and ULH (4 tons titanium), which are mountain guns. The class of guns I'm referring to:
These types of guns can quickly fire and reposition fast enough to avoid CB fire.
Tatra 815-7 is 13 tons.
Look at the second video and tell me how long it will take.
What matters is the PCL-181/SH-15 cannot cross the bridges.
Second point is, most of our army is already forward located, so the guns have already crossed the bridges. It's a problem for the PLA, when they reach the bridge and cannot cross it.