Convert plug-in light to hardwire (not hardwire to plug-in)
You are conflating 12V systems with line-voltage systems

When you say "hardwired lighting", you are actually referring to line-voltage ligthing.  This runs on 120V or 230V (actually, it runs on ~12V but has an onboard conversion module) and must be cabled to the high standards of the electrical code for mains wiring.  This stuff can kill you; if a lamp falls off and drops into a sink of dishes you are washing, you get to see how good your safety protection is on the circuit. 

When you say "plug-in lighting", you are referring to one format of low voltage lighting.  This runs on 12V or 24V, and the electrical code for wiring methods is much more relaxed.  This stuff cannot kill or even shock you.  If it falls into a sink of dirty dishes it will probably remain lit.

Low voltage lighting is better - for safety, for ease of wiring, and for cost - not needing a high voltage conversion module in every light.   

It would pay to do some more learning about these two very different technologies. 

One neat thing about low-voltage is dimming works much, much better in terms of which lights they can dim, and how much they can dim.  That allows you to over-lamp your installation, and back down the brightness to what is comfortable at night, while being able to pump it up for working by day. 

Convert this entire system to low voltage

The problem is, the wiring methods here are a nightmare.  One does not simply put mains wiring through a crevasse in the wall.  It is totally unacceptable as 120/230 mains wiring and must be completely redone at considerable expense, with lots of drywall work.  

On the other hand, this sort of thing is typically acceptable for 12V/24V wiring.  

Plug or hardwire has no bearing on voltage

Plugs or hardwiring are a wiring method, and work on either one.  That means you are free to use hard-wired wiring methods on 12V/24V stuff.