Why are multimeter batteries awkward to replace?
The internals of a well designed handheld multimeter are designed to contain any explosions that may occur from failing parts.
Imagine the following situation: you're holding a meter in your hand, carefully and following all proper safety procedures measuring what you think is a 120 VAC line... and then it turns out that a fault in a transformer somehow managed to put the 13.8 kV distribution voltage on the line. The multimeter is not surviving that; its fuse blows, but not before a MOV catches fire and a few capacitors explode when their electrolyte flash-boils. If the multimeter was designed like any average consumer electronic device, the force from that explosion and the flames from the MOV would shoot out the sides of the meter, likely severely injuring your hand. So all but the cheapest multimeters have their internals tightly sealed, with tall blast walls separating the inside from the outside.
As a consequence of this, anything internal to the meter must also be sealed inside. Have you noticed how the battery compartment has tall walls, instead of just being a flat lid you put over the batteries? This is part of the multimeter's safety design--and sure, a situation like the one described above is very unlikely, but it's still possible, and I'm sure there are more likely scenarios that could accidentally put much higher voltage on the meter than it's meant to handle.
Likewise, that battery compartment needs to be firmly attached to the meter, and that means no plastic clips that will break off after a few uses--it must use screws to secure it in place.