You'll need to deal with scratch start if you do that, which is a bit of PITA, but doable. With real TIG machines (with hi freq start and pulse) so cheap now, scratch start is just another skill that can be frustrating to learn solo. I worked in a couple shops decades ago where the new welders were expected to use old, scratch start (conversions from stick) machines. Without exception, when they graduated to a decent , "real" TIG machine, their weld quality went up noticeably, and I often heard "this is so much easier!!!"
So far as consumables cost...
get a flow meter, and set it at about 15 CFM or a bit less, and get a mini gas lens...that will cut your gas use way down. You wont have a gas valve on the DC power supply, so turn your gas off when not actually welding. Or buy a retrofit TIG kit.
Get a cheap low power cordless drill , and chuck your electrodes in that when sharpening. Hold the electrode near the tip with a cloth glove, and walk the electrode across the grinding wheel so you don't get grooves. Get a wheel dresser to keep it sharp and smooth.