I don't understand why you don't just go all grain. Malt Extract is expensive.
Compare grain @ 70 cents / lb to extract at $3/lb. You can buy 4.5lbs of grain for each pound of extract. The cost savings really add up fast if you brew a lot.
Also, it's such a small size. Why not get into 5 gallon batches? There are lots of advantages to that. Most equipment is designed around 5 gallon batches (or bigger). carboys, buckets, ingredient kits, etc.
You mention the All Grain mess, but it's really not a big deal. You just dump it all into a trash bag and rinse out the MLT... the same thing you'll have to do with your 3 tier setup anyway.
You could do BIAB. That would take your cost way lower and involve less specialized equipment than you are proposing with your oddly-sized 3-tier set up.
When I got back into brewing, I always kept some DME around to do partials, or bump up the gravity of a batch if I didn't reach my OG. But now that things are dialed in and I am no longer using old malt, it seems rather pointless. It really kills your cost savings.
Why not just buy a turkey fryer, a 7 gallon kettle, and do BIAB? Why mess with the 3-tier system? If you are going to create something that requires dedicated space, you should at least get some time or money savings out of it. Otherwise, I agree with your friend, it seems rather silly.
But then again, this is a HOBBY, and if you think this over-sized partial mash system will make you happy, then go for it... but I don't see what you're gaining beyond just doing partial mashes on the stove, or going with BIAB.