Why do some airport towers avoid monitoring 121.5?
It seems to come down to the point that as long as someone is monitoring 121.5 in a specific airspace then not everyone needs to. And it helps avoid multiple ATC facilities responding to the same call. This is from the FAA's Facility Operation and Administration orders (my emphasis):


  3-3-4. EMERGENCY FREQUENCIES 121.5 AND 243.0 MHz  
  
  [...]  
  
  d. When facilities are in proximity and no derogation of services will
  result, transmit/receive capability should not be provided for each
  facility. The following requirements shall be maintained:
  
  
  Geographical area coverage shall not be derogated.
  DF-equipped facilities shall have transmit/receive capability on 121.5 MHz.
  Facilities without emergency frequency capability shall have appropriate landlines for rapid relay of emergency information.
  


Looking at KSJC, there are a lot of other airports close by, so the potential for confusion or conflict on the frequency seems high. My guess is that they leave 121.5 to NorCal TRACON; KPAO is 10 miles from KSJC and also doesn't have 121.5 available, for example.