But even if that was not the case and it could throttle down enough, suicide burn is the most efficient way of landing a rocket (the least amount of fuel required) as it has very small gravity losses - the faster you slow down, the less you have to fight against gravity, so they would use it in most cases.
The amount of fuel left when going anywhere besides low earth orbit (or the international space station) is so big that they hardly have any to spare - the tyrany of the rocket equation and all that... You can test it all out yourself in Kerbal space program :-)
Adding another (different) engine also complicates things. Currently they only have a single engine type for the whole rocket (plus thrusters), the one on the second stage having a different nozzle. This greatly reduces complexity and thus cost and risk.
Mass on the second stage is on the rocket during both 1st and 2nd stage burns, while you get to leave 1st stage mass behind for the 2nd stage burn.