the theory of evolution predicts Broom's observations
So I see Broom's observation that "evolutionary clock has so completely run down" as the well supported claim nowadays too.
Perhaps it has slowed, but to expand on PaulK's second point above, that is not a contradiction of the Theory of Evolution, but rather a prediction of the theory of evolution:
Evolution/speciation is predicted to occur more rapidly when there are many unoccupied niches, which was the exactly the situation after the KT mass extinction. In other words, up until the KT extinction, mammalian evolution was likely as slow as it is today (only two lineages as stated by the 2005 chart you posted). At the mass extinction event, these lineages explosively diversify and speciate (evolve) to fill all of the newly available niches. Once these niches are filled, the diversification again slows, as demonstrated by the posted chart. At that point, most species are generally under normalizing selection to maintain their niche-optimized characteristics (until the enviroment changes), and thus appear to have stopped diversifying/evolving.
These bursts of evolution are often referred to as adaptive radiations, and occur on a much smaller scale as well. The Galapagos finches are perhaps the most famous version of this type of event: A single pair of finches colonized the Galapagos islands, and their descendants evolved over time into fourteen species, each with its own specialized characteristics optimized to the niche it inhabits.
A very important point: Nothing about the Theory of Evolution predicts that diversification of species or lineages should proceed in a regularly timed manner. Instead, such diversification relies on environmental factors (selection), and thus will likely occur in spurts with environmental changes or availability.
Please let me know if you would like any clarification or further explanation. Again - the observation that no new lineages of mammals have arisen since the Eocene is a prediction, not a contradiction, of the Theory of Evolution.