Is it a bad idea to plug the other end of ESD strap to wall ground?
If your ground strap has a proper current limiting resistor, then you would be perfectly fine connecting it directly to ground.

If your ground strap does not have a resistor, then it greatly increases your chances of dying if you connect it directly to ground.  If you don't have a resistor in your ground strap, and you touch a live wire while wearing your ground strap, then you will get full line voltage and current applied to your body - and you won't be able to break the ground connection.



Ground straps are there to drain and prevent a build up of static charge.  You don't need a fast discharge.

A ground strap should have a certain resistance (usually 1 megohm or more.)  That drains any charge on your body, but limits the current in the event you accidentally touch a live wire.

A 1 megohm resistance will drain the charge on your body quickly enough - your body's capacitance is only some few 10s of picofarads.  If you were charged to 10000 V (can easily happen)  then it would take less than 1millisecond to discharge your body through a 1 megohm resistor.  Fast enough.

If you are grounded through a 1 megohm resistor, and touch a live wire (say, 220V ac) then a maximum current of 0.2 milliamperes will flow through your body.  It might tingle if you are exceptionally sensitive, but it won't injure or kill you.