We were unable to get an official response from Caesars Entertainment, so we can only speculate as to the reasoning behind the new regime, but it is worth noting that Caesars Palace, The Cromwell, Nobu Hotel, Paris, and Planet Hollywood all continue to offer round-the-clock room service. (Our speculation, given the findings revealed in this answer, would be that it's all part of the general cost-cutting program to which we'd also attribute yesterday's news regarding the imminent closure of the Rio's Village Seafood Buffet, among other things. It could also be that there was a lack of demand for this amenity.)
Strangely, although Paris shares a physical plant with Bally’s, they do not have identical hours of room service. (More of that in a moment.) The Cromwell is a special case. Its room service is handled by Giada, the only on-site eatery, and offers a menu that's somewhat more exotic than our typical experience of room-service fare. (Think: freshly squeezed grapefruit and mint juice; chia seed parfait; strawberry polenta waffles; and tenderloin slides with pepper jelly, for example). It also comes with an 18% gratuity-plus-tax surcharge.
Room-service hours at the other Caesars properties in town are something of a patchwork. Bally’s, the Flamingo, and The LINQ all now hew to the 6 a.m-1 p.m. schedule you encountered. The Rio, for some reason, is essentially a breakfast-only proposition: 5 a.m.-11 a.m. Harrah’s Las Vegas is also an odd duck, serving from 7 a.m. to 11 a.m. on Sundays through Thursdays, but keeping the kitchen open from 7 a.m. to 9:45 p.m. on Friday and Saturday.
We also conducted a random phone survey of diverse properties around town to find out if Caesars' curtailed hours were an aberration, and indeed this seems to be the case: The Cosmopolitan, Golden Nugget, Green Valley Ranch, Orleans, Venetian, and Wynn Las Vegas all provide room service 24 hours a day.