I think your original point is a good one. The only practical issue I would see is time.. Everyone who is decent is busy, we plan work for our team 2-3 weeks ahead usually, so dropping off to do a check may be tricky at short notice.. but then, an hour is easily fitted in.
Having said that, if you spend the time to teach people (checking engineers) the basics (and thats all a decent engineer needs to understand the principles of the design) then they will appreciate your effort - what comes around, goes around!
On the second point.. we use Excel, beampal and CADS A3D, the later only rarely as its just not commercially viable (or necessary) for every job.
When I started everything was hand written, then we moved everything to excel (I sold my shares in tipex) and things have gotten gradually more and more complex with macros and VB
programming to make them quicker and easier. Wind to Eurocode for example - we spent a lot of time developing an excel sheet to to this (not a fan of dumbed down TG20 option).. and its worth every minute.