The initial reason I purchased an amp was that I had people over and had the volume cranked way up and all of a sudden "pop" and the AVR shut down. I didn't want to ever have that happen again with the risk of damaging my speakers. We may have been listening to multi-channel audio at the time. My speakers are relatively inefficient - I think 87dB/W.
My secondary justification for getting an amp (ended up being 2 ATI amps - both used at great prices) was that I'd never have to buy a more expensive AVR that had all the amps internally in order to power the 11 speakers I use for ATMOS and DTS Surround. I thought it would be a waste of money to have to buy a more expensive AVR for extra internal amps every time I upgraded my system. At the time, I would have had to upgrade to the flagship AVR to run things - the cost difference paid for my separate amps. Even today, I would have to purchase the Denon 6500 (Retail $2,199) instead of the Denon 4500 ($1,599 retail which has 2 more internal amps than my 4300) to power all my speakers which would have cost an extra $600. If you upgrade your AVR every few years, that internal amp premium adds up very fast.
Another reason I purchased the amps was that I thought I'd have better sound quality with the flagship Marantz 8802. It turned out in blind testing
that me and other AVSers did that we couldn't hear any difference in audio quality so I won't ever buy a flagship Pre/Pro or AVR unless it offers some special format or audio calibration feature that will give a tangible improvement that I can actually hear.
Given my two used ATI amps (200W x 5 and 180W x 7) were about $1,500 combined, I'm happy with the choice. They are great amps and I don't think I'd lose money selling them. I don't think they improve the sound quality at all but I do find comfort that they'll never run out of headroom in my system. My biggest dislike of the amps is that they generate a lot of heat. I have a relatively small theater and had to move my AVR stuff into a closet due to the amount of heat they generated which made it uncomfortable in the summer as I didn't have enough air conditioning capacity in the room to offset the heat generated by several people, a projector and all my AV equipment. I had to cut an open access panel in the ceiling in the closet (which I leave open) to allow the heat to escape into the the joists between our lower level and main floor.
If you're not listening loud with inefficient speakers, a basic mid-range AVR will likely drive that setup but certainly worth considering an amp to save money over time.
You've got a great setup you're contemplating. Sound treatments are a huge deal and probably have the best bang for the buck for sound quality. Contact GIK for ideas and prices as you can improve in that area as your budget allows or go DIY. I used both GIK and DIY.
Also, I've got a similar size room (12 x 16) and have gone through many subs over the years. I'm now at dual PSA S3600 subs (4 - 18" drivers). While they are incredible, I would have gone ported for more tactile response if I had room for ported subs. #1
advice: get the biggest, baddest sub you can afford and then hope your budget allows you to go dual down the road. It gets expensive to keep upgrading all the time as I did. I ran multi-sub optimizer for my room using actual measured alternate sub locations and more subs won't actually improve my sound quality other than give me a bit more headroom which I don't really need as I am quite a bit over reference and can already shake the house. My Crowsons thankfully help for tactile response.
Good luck moving forward!