My opinion is less professionally-qualified than Vistet's , but based on many year's experience of La Paz (including for some time responsibility for the well-being of official visitors) I would summarize as follows:
The standard recommendation in the outfit I worked for was that all arrivals from sea level should rest for the first 24 hours. This recommendation was usually ignored, for reasons of time. Additional recommendations were to eat little in the evening, drink plenty of water but no alcohol. And to sleep unaccompanied.
Most (indeed almost all) arrivals in La Paz from sea level experienced mild AMS (please excuse paradox) for a day or two - breathlessness walking even slightly uphill, a headache, irregular sleeping patterns (check out "Cheyne-Stokes Breathing"). However, usually this was no more than an inconvenience for a couple of days.
Vistet is quite right in saying that age and fitness are irrelevant (well, unless the person has heart problems or is suffering from the consequences of heavy smoking, for instance). I recall overweight people in their 50's and 60's who were less affected than much younger people.
I have seen a small percentage where symptoms were more acute. This should be taken seriously, and immediate descent to a lower altitude is the solution.
Although this is difficult to demonstrate objectively, I do think that in some cases there was a psychological element where someone arrived expecting to be seriously ill and had his or her fears apparently confirmed by the appearance of the mild symptoms which are normal.
Another contributing factor is that many travellers arrive at El Alto airport either in the wee small hours of the night or at 6 a.m. after an overnight flight from Miami. On top of that, if arriving from Europe they are jet-lagged. So even without altitude, they probably feel below par (a more colourful term might invite the attention of the moderators!) .
Of course if you were to stop over for a night somewhere a bit lower than La Paz (Bogota, for instance) it would help acclimatization, but on the whole IMO there's no need to worry overmuch. Most visitors seem to survive! If you look over this forum, for instance, you will see that threads on the subject start with enquiries from posters who have had no experience of high altitude. I don't recall many saying that they nearly died and had to be evacuated.