Do studs in wooden buildings eventually get replaced as they lose their structural capacity?
No.
Wood frame construction is generally done for rigidity not strength.  You can climb a tree and have the branches deflect significantly before they break - the strength is fine - if you build a house with just strength in mind then you'd be bouncing all over the place.  Wood frame construction is instead designed for rigidity such that when you walk across the floor your book case isn't bouncing up and down.
You also have to take into account that a lot of walls are not strictly part of the structure.  A lot of interior walls are only there to delineate spaces.
Now getting into the drilling a million holes over the years into studs such that they eventually fail.  Studs are under compression but are very strong in compression.  Rules for how you can notch or drill studs typically allow quite large holes for water pipes and  waste water pipes.
&quot;Holes in bearing wall studs may not exceed 40 percent of the width of the stud.  Holes in non-bearing walls can’t exceed 60 percent of their width.&quot;
https://www.familyhandyman.com/project/drilling-holes-notching-and-boring-holes-in-wood-studs
Now given you can drill a hole 40% the width of the stud in a bearing wall, 40% of 3.5&quot; width = 1.4&quot; (~1 3/8).  How many 1/8&quot; holes does it take to equal 1 3/8&quot; = 11 just to form the diameter of the allowable hole.  I am not going to do the math on how many it would take to equal the full hole.  These holes would all have to be in the same area to achieve the accepted weakening of this member.  Now factor in that the full strength of the wall assembly at the weakened state is likely only required under 100 year design event conditions and like most things dictated by code we reach a factor of over engineering which should ensure safety and there should be no way you could drill enough holes in the lifetime of a building to put the structural integrity at risk.
A plumber or electrician drilling willy nilly through load bearing members is a different story - even then you likely only encounter problems at design conditions.