The curious thing is what happened before the internet?
Well here's a pre-internet (Sibson c. 1980) account.
The school would print off the Notams (ususally 3-5 pages) and pin them to the notice board. Then, they would pin on top a raggedy torn piece of paper saying "No royal flight today" or occasionally "Royal flight today". (The 3-5 pages was for the whole UK and might be compared with the 12+ pages of today's 'area brief').
If there was a purple airway, one would certainly plot it out to see if there might be a conflict. The Notams in those days were hand compiled, concise, and relevant.
We certainly did read the rest of the Notams, but time pressure prior to flight often made that a presumptory affair. A huge breakthrough came at the end of the 90's when the same hand crafted Notam report became available at home over the new fangled Internet allowing every Notam (No need to say 'relevant' because in those hand crafted days they were all relevant) to be studied properly.
Then of course the hand crafted Notams were snatched away to be replaced by the present bureacratic shambles.
Strange how reminiscent of those far-off days the present 'Lockheed Martin' flight service is. The briefer plots your route and checks for Notams. He or she advises you that there are no TFR's close to your route, or makes sure you understand if there are. Then he or she goes through the rest saying "are you interested in x or y?", constantly filtering for relevance. Just like our old, hand compiled, Notams back home.
Still, presumably the present UK system costs the UK taxpayer far less money than either the old hand crafted system or (pro rata) the spendthrift Americans' private FSS contract. Obviously.