You appear to have missed the point of the original author entirely. He brings up specialization as an alternative precisely because those who attempt to become the broad based founts of knowledge have to study so much longer now than their predecessors. The depth of every field of knowledge is deeper now than during the Renaissance, so the initial task of "climbing onto the shoulders of giants" takes correspondingly longer.

The best way to address that problem is find ways to drastically extend human lifespan and expand the ability of humans to organize and retrieve knowledge from our brains. However, it appears we have more pressing issues in front of us for the immediate moment.

Anyway, the key point is that before you can stand on the shoulders of giants you must first get onto those shoulders (acquire the existing knowledge base) and since it has grown deeper and deeper, it takes longer and longer to make that climb.

I don't think he missed it, he just did not think we took the right path to deal with the problem. And specialization turns to be the greatest problem of any structure over time. Because it develops rough and hard to change structures that are productive in the short term, but tend to break whenever something in their environment changes.

Now we seem to be in the trap of deminishing returns from the technology, but first we should realise that our ways are wrong so that we start looking for other ways. I've been educated within a system that did not favor specialisation, quite the opposite in fact. The results were very... mixed. First of all lower productivity - an open minded person is much more prone to reflection than happily following the commands in some hierarchical structure. Second there is a great frustration when you go out of school and start to deal with reality. Third - weak higher education. I think there were thousands and thousands of people that had the potential for their breaktroughs and their Nobel prizes -  versatality makes wonders with human minds. But they did not meet anybody on their way out of the school and most ended up as economists or programmers.

My view is that the major flaw of our system is that we are trying to let out entropy with it. Instead of trying to live with entropy, learn its rules and cope with them... we have lived in a meager second of the lifetime of this planet and we already received the self-esteem of unkrowned Gods. This will not and can not end well.

For a comprehensive analysis of diminishing returns to complexity I would recommend a fascinating archaelogical study called The Collapse of Complex Civilizations by Joseph A Tainter (Cambridge University Press, 1988). The entire work is very much worth reading in my opinion, but I would especially recommend the final section (pgs 209-216) on the contemporary situation.
Imagine a Giant Dung Ball rolling down a shallow hill ... towards a cliff.

Inside the Giant Dung Ball, all sorts of dung beetles (scarabs) are busy with their specialized niches.

The acountant beetles are busy counting dung beans.
... all is well in their specialized universe.

The financial markets beetles are busy projecting "expectations" for the next quarter.
... all is well in their specialized universe.

The politician beetles are busy collecting votes for the next election.
... all is well in their specialized universe.

The next-specialty beetles are busy doing their dung-centric speciality with eyes focused only on their niche. All is well in that niche too.

No "specialist" is responsible for steering the Giant Dung Ball as it "progresses" down that shallow hill ... towards the cliff!!!

Of course you understand the metaphor.
Planet Earth is the Giant Dung Ball.
"We" are the dung-brained beetles who are busy weaving our niche-centerd doom inside the Ball.

All is well inside each of our "specialized" niches.

Adam Smith was such a genius.

(An Image of "Atlas" as the only entity responsible for our teetering globe:
http://www.nso.lt/bible/atlas.jpg )

In classical Adam Smith economics, the dung beetles would have a specialist class of dung beetles to invest in new technologies found by the specialist class of dung beetles that invent new technologies to find new balls of dung.
Truth is better than fiction.

We have a specialist class of denial beetles:

http://www.insultsunpunished.com/2005/10/18/peak-oil/

Their job is to weave bales of dung into threads of golden words that will allay the fears of the other beetles.

Good job boys.

Keep up the efficient conversion of BS into more BS.

The supply of clueless cornucopians is the one thing that some days does seem to be effectively infinite. Don't they feel any need to research the issue at least a little bit before taking a position?
True Believers of the Adam Smith religion
NEVER question the DOGMA

The "markets" will provide.

Always have.
Why worry about science and such?
There is an infinite supply of techno-nerds (cheap Dilbert kinds) and solutions.