Fig. 3:  Times Roman is the most widely used of all Transitional fonts---and probably even of all existing fonts

It is difficult to name just one reason for this phenomenon.  Who could say, was it that Times was chosen as the basic computer typeface because of its neutral character, or on the opposite, we perceive it as neutral because we got used to seeing it everywhere? I think that indeed it was the transitional period when the best possible balance was achieved between the freedom and even looseness of Old Style and the mannered rigidity of the new type of 19th century. That new, sometimes even called "revolutionary," font design created at the very end of 18th century and dominating throughout the 19th century was, quite naturally, called Modern or New Antiqua.  (There are other examples when some intermediate stage in the history of art becomes forever termed "the newest"; for another instance, "art nouveau," which means "new art," was current in late 19th century and then obsoleted by other movements---but kept its name.)  This style has further developed some of the transitional trends, but decidedly abandoned some others.

Fig. 4:  Use Modern typefaces to create an old-fashioned look (pun inevitable)

In particular, Modern fonts have drastically increased contrast, leading this parameter almost to the edge of legibility and technical feasibility (in fact, one of the inventors of the new style, Giambattista Bodoni, had to improve the printing machinery he had available in order to reproduce the new fonts).  The long, hairline serifs and horizontal strokes are the first thing we notice about this font style, although it has some peculiarities in the shapes of letters as well. Due to the high contrast and the lack of almost any coves and rounded corners, the feeling conveyed by Modern fonts is very dry, rigid, elaborate, even unnatural.  Although Modern has an easily recognizable style of its own, my opinion is that this font design is a dead end in the history of type, because, in at least one aspect, it has achieved a limit that cannot be pushed any more without losing some essential characteristics of letters. This might be considered truly ironic that the fonts that were once hailed as a revolutionary improvement and called "modern," now are perceived so distinctively obsolete and out-of-fashion.  Perhaps that's because this font design was the last to lose dominance, its dislodging took place within our recollection, and we therefore tend to associate it with our direct predecessors, the "parents generation"---which is always divided by a wider generation gap from our own than those who happened to live centuries ago.  But maybe the reason is simpler, and the spiral of history has brought us to a point where we're much closer to the harmony and open spirit of Renaissance than to the self-assuredness and mannerism of the 19th century. Despite what I said about the "dead end", Modern has in fact served as a base for several design variations created throughout the 19th century, the most notable being slab serif fonts where serifs were as wide as main strokes or even wider, and later, clarendon fonts that re-introduced cove serifs and lowered contrast while preserving the overall style of Modern letterforms (New Century Schoolbook is the most widely used Clarendon font).  Both classic Modern faces and their derivatives have pretty much dominated the typography scene in the 19th---and well into 20th---centuries. However, it didn't take some new and fashionable design style to replace Modern faces in the mass book production.  Instead, the century now drawing to a close was marked by an unprecedented wave of revivals---fonts created from ancient prototypes of the Old Style, Transitional, and early Modern ages.  It wasn't long ago that the now ubiquitous Times, Baskerville, Garamond, Bodoni were recreated, using a varying degree of generalization and modernization, by our century's font artists from old printouts and printing matrices.  Now the spectrum of digitized serif typefaces is wider than ever; dominated by revivals, it also contains a plethora of original faces, for both body text and display setting, combining modern trends with the best features of all previous ages of typography.