System Information
Operating system: Windows-7-6.1.7601-SP1 64 Bits
Graphics card: AMD Radeon HD 6290 Graphics ATI Technologies Inc. 4.5.13399 Core Profile Context 15.200.1062.1004

Blender Version
Broken: version: 2.81 (sub 13), branch: master, commit date: 2019-10-04 13:28, hash: rBd590db83705b
Worked: (non-applicable. 2.79b has the same problem)

Short description of error
As much as working with the modifier stack as much as possible is encouraged, one issue happens with the Subdivision Surface modifier: the modded mesh blocks the base mesh in edit mode, as shown here:

This makes selections of single vertices pretty much impossible, since a selection like this:

Is completely hidden with the modifier activated:

The same happens with edge and face selections:

Switching to X-Ray mode has its own set of issues. Selecting anything precisely is very hard due to the two meshes "overlapping" and you having the added "benefit" of being able to select back faces accidentally due to the extremely minimal visuals that are the same color as everything else when not selected:

Changing from Subdivision Surface to Multiresolution introduces other problems. While there are no issues concerning Edit Mode, you lose the visual feedback if you're controlling the mesh by editing the weight as only the base mesh is displayed. You also lose the bevel modifier workflow of controlling the weight and your only visual feedback for creasing is the color change from black to purple, which is fine for 0 or 1 scenarios, but not so much if you're doing small tweaks, as you have to constantly switch between Object and Edit modes to check the changes.