Yes, we can ask you to plan your landing roll in a certain way. We won't technically instruct you to brake the aircraft in a specific way, but simply to aim for a specific taxiway after landing.
There can be different reasons for this, but generally it is an attempt to expedite traffic flow on the ground at the airport. For example, if you are landing on a long runway and your parking position is near the far end of the runway, I might ask you to keep the plane rolling down the runway and vacate at the end, in order for you to have a shorter taxi time.
It could also be that the taxiway you would normally use to leave the runway is blocked by another aircraft or vehicle, and I want you to leave the runway via a taxiway that is further down the runway.
However, extending the landing roll does extend the runway occupancy time as well, so if there is another aircraft behind you on short final I will not offer you to perform a long landing roll. This is also why you should always ask ATC if you are planning to perform a long landing for one reason or the other – if we have someone else just a couple miles behind you, we might have to instruct them to go around if you do not vacate the runway like we expect you to.
With regards to reverse thrust specifically, there are airports where the use of reverse thrust is only permitted in special situations. This is to reduce the noise level at and around the airport. However, this is purely a regulatory thing, and is not actually related to ATC.
ICAO offers the following guidance on the subject (DOC 4444):
18.104.22.168 When necessary or desirable in order to expedite traffic, a landing aircraft may be requested to:
a) hold short of an intersecting runway after landing;
b) land beyond the touchdown zone of the runway;
c) vacate the runway at a specified exit taxiway;
d) expedite vacating the runway.
22.214.171.124 In requesting a landing aircraft to perform a specific landing and/or roll-out manoeuvre, the type of aircraft, runway length, location of exit taxiways, reported braking action on runway and taxiway, and prevailing meteorological conditions shall be considered. A HEAVY aircraft shall not be requested to land beyond the touchdown zone of a runway.