Is physics education at that bad level?
y guess is that the charge that has been built-up will eventually degrade and cause no damage.
Yes, but a static charge dissipates quickly
Pretty much wrong both.
Static electricity is typically created when
different non (/badly) conducting materials rub each others which causes transfer of electrons from one to another and leads to equal but opposite electric charges being stored in them. If air is dry and pure (humidity and impurities lower resistance) charge can continue building up and be stored for quite long time unless otherwise neutralized.
If either of these now charged objects touches, or comes close enough to exceed air's strike through voltage (~3kV/mm for dry air), any conductive object in different potential there happens electrostatic discharge (ESD) which either balances potential between source and target or completely neutralizes electric charge if target object is grounded.
With very strong electric charge already electrostatic field of charged object can cause damage to non grounded sensitive electronics by creating potential differences in it.
Will that not just prevent a component getting a static charge in the first place? I guess when I pick up the component I will get the static charge and ground it through the strap but I'm not sure though
In this situation (and always with computer parts) the problem isn't the component but you.
In dry environment human body (and clothes) can fast collect big electrostatic charge if surfaces are non conductive.
After that touching any conductive object causes sudden electrostatic discharge and nothing can protect sensitive electronics when it's left in route of this discharge.
Antistatic strap connected to ground prevents build up of this dangerous electrostatic charge and keeps you in neutral potential. (straps serial resistor also neutralizes charged objects you touch without sudden discharge)
Also when putting components into case it's better to first touch metal structure of case with skin in some part of your body so that possible charge/potential difference is balanced/neutralized trough you instead of by ESD trough component being installed. Keeping case grounded can prevent this problem but still exposes components to ESD unless you're yourself grounded similarly. (keyword is same neutral potential)
Antistatic bag protects components inside it because Faraday cage keeps electric charges outside of it.
Here's some experiments
http://www.sciencemadesimple.com/static.html
Also if you have electrically insulating floor or carpet on it (shoes work also) and for example wooden varnished table you can easily generate nice amounts of static electricity. (and below -10C weather is good, then air is much drier than in Sahara)
When all is clear and there aren't flammable fumes around just take one paper sheet from printer and start rubbing it against table's surface with your hand and after few minutes (the more the better) touch some electrically conductive object, also because like charges repel each others corners of object have highest charge levels so finger tip is best...
But don't come to complain if it hurts!
There's no burn marks on any components so the only thing that comes to mind is static (lighting is basically a form of static electricity isn't it?)
Charge which is discharged in lightnings bolts is probably created by process similar to static electricity but scale is entirely different, both voltage and electric charge.
Current of lightning is measured pretty much in tens of kiloamperes. Strength depends much on climate of area because stronger thunderstorms naturally generate stronger electric charges but bolts up to 50kA should be possible pretty much in all areas. Total energy in lightning discharge is measured in millions of Joules and direct hit of stronger multiple strike can vaporize water exploding tree, split stones and instantly vaporize metal from utility lines and electric wiring of your house.
Also rapid pulse of very high current creates equally fast changing magnetic field which will induce current/voltage to every conducting object (including electric and phone cables) close to it.
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