A really simply, no-frills implementation would be that units conducting attacks steadily lose readiness and morale - unless you have a REP battalion, in which case it soaks all the readiness damage and there is no morale damage. Even something as low as 1%/battalion/5days would cause a division to deplete a REP in 20 days of fighting. Numbers would be easy to adjust. I imagine this has the advantage of being relatively easy to code while accomplishing the goal of encouraging a logistics tail.
Complicate it slightly: REPs no longer heals friendly ground forces, but natural replenishment rates are much higher on worlds with (idle?)training facilities. Rename REP to LOG.
There's a lot of places you could go from there. For example, attacks could be of varying intensity, scaling casualties and supply consumption. Cautious/Aggressive/Intense, with 1x/1.25x/1.5x intensity and 1x/2x/3x supply consumption.
Units actively suppressing dissent/occupying non-imperial pops could have low-grade degredation; Imperial populations with low dissent (<5%?) and GFTFs eliminate this attrition. This would encourage the establishment of 'military base' colonies on conquered worlds, especially if you plan to never imperialize the populace. That seems like an interesting path in the Crusade campaign actually. I don't know about you guys but I virtually never loot or 'Imperialize' conquered worlds.
Different unit types could also have differing supply consumption, and maybe even different bonuses for intensities. New systems also open up new unit roles: Commando infantry who suffer less from lack of supplies, and Artillery could be a reasonably strong unit that consumes enormous amounts of supplies.
My personal 'Gamer Gone Wild!' implementation would be to basically lift the system from Hearts of Iron III/Victoria II. Units line up on a pseudo-battlefield, dealing damage to the unit across from them (or diagonal to them) until they are too damaged and fall out of the fight. Artillery has the advantage of being able to attack from the back line. The pseudo battlefield only has a limited width, so artillery is an advantage in large scale conflicts.
Planets could be divided into a number of regions, depending on the size of the world. Colonies would be located in one or more regions. And, and, and... okay i'll stop now.
Actually no wait. I'm reminded of Master of Orion 3. For all its faults, it had a decent model for abstracted-yet-sorta-fun ground combats. No logistics, but combats could rage back and forth across the surface of a planet. As I recall, units had # of attacks, attack strength, armor, hp etc. values that varied with unit type, plus a number of minor stats. Regions had different terrain types ranging from plains to caverns and different units/races had differing advantages in each. Hmm-mmm....
P.S. Ground forces could really use higher upkeep costs. Heh.
P.P.S. I'm not really a fan of artillery, it doesn't make sense to me in a TN context. And to the extent it does how does it differ from orbital bombardment? (Which you can do from PDCs, anyway!)