Grounding yourself is always a quick discharge (causes damage), hense it has nothing to do With ESD-protection at all..
Everything in the pc is grounded through the PSU's earth wire, this is used to trip circuits cutting power and to safely direct current away, this also works to discharge static. Every time you unplug and move your computer around you will likely be giving it a static charge, by your logic plugging it in again and grounding it is going to cause a fast static discharge damaging the computer.
You talk about ESD but have yet to mention resistance or insulation, maybe the most important factors to consider when talking about static. Static builds up because an object has too much resistance around it (insulated), electricity moves like water though the path of least resistance, but if the resistance is too high then it is unable to move and builds until it is able to overcome that resistance, this means the object is insulated by an insulator. When using a wrist strap connected to a pc you create a path of low resistance as the wire has a much lower resistance than skin, clothing or whatever else is likely to be connecting between you and the pc or its components, so static can move between you and the pc through the wire and not potentially sensitive components. Static does not damage components over time, anyway static will be discharged as soon as the pc in plugged in through the psu earth, static causes damage by flowing through a component which enough current to cause it damage. To cause damage the current would need to be strong enough and it would have to be taking the path of least resistance through the component and a specific part sensitive enough to be damaged, for this to happen you would need to be very unlucky. Components come in ESD bags because packaging is not usually very conductive (insulator), in transit the packaging and contents move and rub against each other causing static charge to build up which may be discharge in a way that could cause damage once opened, an ESD bag keeps that static off the component. As far as I know stasis does not move slowly and gently, it builds up until it overcomes resistance and discharges, I imagine as its electricity it moves at the same speed.