In your example, the specialized science city has Oxford/library/univ/observatory. This city almost certainly has very few , and cranking out those buildings is going to be a problem.
Generally speaking, the Bureau capital has a few non-cottage improvements at the point of getting Education (usually bulbed in my bureau-capital games). For example, when whipping universities in other cities as well as building them in high

cities, the capital still has a couple mines and a couple workshops on non-riverside grassland. Even if the raw

is only 12, with bureaucracy, it's 18 and I can generally secure a stone resource by the time I'm building Oxford, therefore 30

/turn. A couple forest chops helps the capital complete Oxford in less time.
I'm sure you're not suggesting that the turns required to build Oxford makes non-specializing of the empire more desirable. Investing a few more turns to get that bureau-capital Oxfordized (lol) is much more worth it IMO. After building it, build cottages over the couple workshops and grassland hills and put windmills on any plains hills. This generally allows for anywhere from 16-18 cottages in a good bureau-capital site.
Honestly, I get it, though. Non-specialization is
viable. But OP is saying it is a bad idea. That non-specialization would essential beat specializing outright. It takes a very specific (and very difficult) map situation for this to be true.
Also, let's not forget specializing hammer heavy cities. After I get 2-3 cottage spam cities (other than my capital), other mostly-green cities will get workshops put down wherever possible along with mines and watermills. Those specialized cities serve 2 purposes: 1) Build military and spies in a time of war preparations and 2) build "wealth" in times of peace/tech-surging to keep slider @ 100% for as long as possible to allow that bureaucracy capital to maximize it's science output.
Also in my specialized empire, Every city should get the food and hammer boosting buildings like Granary, lighthouse, AP buildings, forge as priority builds; which in turn facilitate all future whips/builds. It is a very simple concept.
Yeah, buildings like Granary/Forge should be in all cities since granary helps grow population much faster and forge is a requirement for IW and also adds

for gold/silver (not to mention the 25%

boost). Lighthouses in coastal cities, but I honestly leave off the AP buildings for my "hammer" cities. The AP hammer boost is only something I invest

on if the city is specialized for hammer output.