You've raised several issues that, while interlinked, are separate.
1) Escorted tour vs. My Way tour vs. do it yourself. There are pros and cons to each approach. But be careful - many people will have strong opinions on things they have not done. I'm in this category myself - I don't think I'd like an escorted tour, but I've never taken one. I am struck, however, by the number of people on this forum who have traveled independently, and still love Rick's escorted tours.
2) How to see Spain in a short time. It's a large country, with three main areas of interest for first timer visitors - Barcelona and around, Madrid and around, and Andalucia. On the one hand, Barcelona to Madrid and Madrid to Seville are each only 3 hours by high speed trains, so these regions are easy to connect. On the other hand, there's lots to see in each of the three, so on a short trip, you can chose between doing a taste of all three, or just doing one or two with a bit more breathing room.
If you do want to see all three in 10 nights, you'll do better with some form of tour, for the reasons you mentioned - it takes care of the logistics, so you can be more efficient.
And I also leave on a Thursday and return on a Monday (10 nights in Europe) - works great for me! However, I take two of these trips a year. So, I always plan to see just a small area on each trip. For my four trips to Spain so far: my first trip (1995) was Madrid and Barcelona. My second trip (2006) was Andalucia (overnights in Seville, Cordoba, Granada, and then one night in Malaga to get the flight home). My third trip (2015) was Madrid, Toledo, and Barcelona (not only had it been 20 years, but I made some mistakes on the first trip and corrected them). And my fourth trip (2017) was Basque country of France and Spain.
What were my mistakes on that first trip?
1) I was in Madrid over a long holiday weekend but didn't know it. May 1 is a Europe-wide holiday, and May 2 is a local holiday. I only realized what I was missing when the holiday ended (as I was leaving) and felt the difference when everyone came back.
2) I saw the Prado my first, jet-lagged day. On my second trip, I deliberately waited until my last Madrid day to go to the Prado. Much better - not only was I fully awake, but after the Prado, all art will seem second-best, so I saved the best for last.
3) I went to Toledo on a Monday - when lots of things there are closed. For my second trip, I stayed over a Tuesday night.