Will primes become rarer in the 24-70mm range for DSLRs like they did for the 70-200mm?
Probably not. The biggest advantage of most primes in the 24-70mm range is the wider than f/2.8 aperture to which the zooms, for the most part, are limited. Most telephoto primes past 200mm do not share that advantage.
There are also many prime lenses in that range that, while not cheap, provide image quality that even the best 24-70 f/2.8 lenses can't touch. The Zeiss Otus series, for example.
On the other end of the scale, consumer grade primes in the 24-70mm space can provide wider apertures and image quality that rivals or bests the premium zoom lenses at a fraction of the price.
This is not so much the case with telephoto lenses, where larger apertures require entrance pupils that significantly increase the size and weight of the lens. A 200mm f/2 requires a front element just as large as a 400mm f/4!
Telephoto zoom lenses are also easier to design since the entire focal length range is a telephoto design. Most 24-70mm zoom lenses start out at 24mm as retrofocus designs and shift to telephoto by 70mm. This highly complicates things.
Higher magnification also requires better optical design and precision manufacturing for the same image quality that can be had from shorter lenses with looser tolerances. As super telephoto lenses beginning at 300mm make it abundantly clear, even a prime lens with that much glass in it can be quite expensive. A 135mm f/2 typically costs as much or more than a 70-200mm f/4. So the advantage of price disappears somewhere between 100mm and 135mm for lenses designed for cameras with the 36x24mm format.
The reason there haven't been a who lot of updates for existing prime lenses in the 24-70mm lengths can probably be partially attributed to the relative maturity of the designs in that range that have been around for a couple of decades. The few updates that have been released by Canon, for instance, either add a non-optical feature such as IS (EF 24mm f/2.8 IS, EF 28mm f/2.8 IS, and 35mm f/2 IS introduced in 2012), a new AF motor type (EF 50mm f/1.8 STM introduced in 2015), or make significant improvements to things such as lens coatings that improve the lens' performance in certain challenging conditions (EF 35mm f/1.4 L II introduced in 2015).
Update: In retrospect, part of the reason we weren't seeing much lens activity from at least Canon and Nikon in the years leading up to 2017 when this question was asked is because they had shifted a lot of their lens development resources to their new yet to be announced mirrorless systems. I'm not as familiar with Nikon as with Canon, but in the past couple of years beginning in the second half of 2018 Canon has introduced 35mm, 50mm, and two 85mm prime lenses among the 11 lenses introduced so far in the RF mount with a 20mm registration distance that is much shorter than the EF mount 44mm registration distance.