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.
If your wrist strap has built-in resistance, there's nothing wrong with connecting it to mains ground or PSU chassis.
However, if your wrist strap is just a conductor and you happen to touch a live wire, the strap will provide a low-resistance path to ground. This will result in a very intense shock, compared to cases where the current has to go through significant resistance along its path (like your shoes/clothes) and thus is much smaller.
In addition to the caveat of having a resistor built-in so that you don't electrocute yourself if you happen to find a live wire, there's also the question of whether the grounding point that you've found is actually ground.
Consider old construction that's been upgraded a few times and grandfathered into the electrical code. It's grossly illegal to build anything new like that, but it's allowed to stay because it was to code when it was built. So you may have anything inside the walls depending on its age, some of which don't have a ground wire at all, and may be difficult to tell at a glance which is live and which is neutral.
Technically, it's illegal in most codes to create a "bootlegged ground" - that is, to connect the neutral and ground terminals of an outlet both to neutral - but it's frighteningly common anyway, and a cheap 3-prong tester won't show it as anything wrong. But the load current makes the neutral wire not ground anymore, and if it were to break, then the end attached to the outlet would suddenly become live via the load. And if it's bootlegged, then the "ground" also becomes live along with it.
Now consider a polarity-reversed bootlegged ground. If it's difficult to tell which wire is what and it takes more effort to test them than the sparky can give, then you have a 50/50 chance of having it backwards. Now the bootlegged "ground" is connected directly to live! And a cheap 3-prong tester will still think that it's okay! (because the neutral and ground terminals are still connected to each other, which is all it cares about)
Then you plug your grounding strap into what you think is ground...