The consequences of a high speed touchdown / high vertical speed are very much obvious. However, what will the consequences be of a low speed touchdown? How severe are they (if any)?
This is certainly not a comprehensive answer but can get you started. I’m assuming fixed wing non-VTOL aircraft.
A low (forward) speed touchdown, all other things being as close to nominal as possible in that scenario, translates in all likelihood to a steeper than normal landing and can be associated with loss of sufficient lift or even stall and can result in a hard landing or crash. If trying to compensate for loss of lift, the same scenario will lead to a higher pitch than normal and thus add (or replace the above with) a tail strike risk.
A low vertical speed touchdown, all other things being as close to nominal as possible in that scenario, means a shallower trajectory than normal and can be associated with a long flare or a deep landing and as such poses risks around stopping performance (e.g. if the touchdown is so soft that the automatic deceleration systems don’t even realise the aircraft is on ground) or available stopping distance (if all the runway is used up trying to stick the aircraft down, none is left for rollout). Exiting the runway down the far end at substantial speed again is a recipe for significant damage and danger for life.
A touchdown with both (too) low forward and (too) low vertical speed doesn’t really exist, as that would mean a touchdown roughly along the nominal path but with lower speed, and since approach speed is usually calculated to be somewhere around minimum safe speed (i.e. stall speed plus some margin), slowing down significantly means stall, at which point the scenario changes to low forward but high vertical speed at touchdown.
I'm going to assume "low speed touchdown" means making ground contact at a slower airspeed than normal. Insofar as it can be done safely, slower=better; less energy to dissipate, shorter landing distance etc etc.
"Can be done safely" is the key phrase. Propeller driven airplanes, especially those that are designed for Short Take Off and Landing operations, can use high lift devices and power to slow to a lower airspeed than normal in order to touch down at the lowest possible speed. It's a specialized procedure because there are some risks; the power is being used to manage sink rate and quite a lot of if is required to overcome all the drag of a slow speed STOL approach. Also you are closer to stall speed. There is little margin for error if something goes wrong with that power. The result, if things go off the rails, is a high sink rate touchdown which may or may not damage the airplane. But, you are doing it on purpose and you accept the risk.
Aside from that kind of specialized technique, "lower speed than normal" (as I would phrase it) at touchdown is not a good thing to strive for because the aircraft needs to have a margin of surplus energy through the landing flare to allow the pilot to regulate sink rate without power in the final seconds. That is, when you flare for landing, you are trading inertial energy for increased lift (pitching up during the flare) to reduce sink rate and manage that sink rate until the touchdown. This is especially true for jets, where you generally can't use power through the landing flare as you can with a propeller airplane, because engines must be at idle before touchdown for the lift dump system to work properly.
So if you are slower than you should be, there is very little surplus energy available and if high sink rate develops there is no way to reduce it (it's too late for power to help). Especially in a jet, you don't want to be much below "reference speed" (full flap approach speed) when you start the flare because at that point, with engines at idle, you are touching down no matter what and if you are too slow, some or all of your intertial energy surplus is gone and the pitch up during the flare may not slow the sink rate at all. Then it's BANG, and off to maintenance for a hard landing inspection. Some jets are more forgiving of being under-speed than others. Those with slat systems and multi element flaps are quite draggy in the landing configuration and bleed energy very fast. Cleaner jets with hard leading edges and simpler flap systems can be actually a bit more forgiving of being too slow because they don't decelerate as fast when the thrust is brought to idle.
Large turboprops are different in that power from that big propeller disc has a huge direct impact on sink rate and on deceleration, and on some you carry power right into the landing flare and may use the feathering off of power to control the touchdown (you land a Q400, which has limited nose up pitch angle, that way). Even there though, if you are too slow, high sink rates may develop that you can't catch in time, and wham.
So bottom line I guess is, there is a sweet spot speed for each airplane to be able to land as slow as possible while still having adequate safety margins via a little bit of surplus energy, and the main penalty for failing to observe that speed is high sink rates resulting in hard landings.