I think that how you feel about staying in Alberto’s apartment is going to correlate directly with how you feel about noise, cooking, Monteverde, and walking.
The noise problem is real. The walls in both the bedroom and the living room are thin, the neighbors appear to be fond of listening to the TV at high volume, and though Alberto spoke to his neighbors on my behalf (I finally said something to him after my third night of their blaring the TV past midnight), that only chilled them out for a day or two.
Though the appliances and plumbing in the apartment worked well (microwave, stove, washer/dryer, shower), the kitchen isn’t well prepared for guests who actually plan on cooking. No containers, one dish towel, a slim assortment of pots and lids that only sometimes fit one another. When I mentioned to Alberto that there was no paring knife or chef’s knife—just a serrated bread knife—he looked at me like I was crazy. (Might have been a language barrier?) I went across the street and bought a 4-euro chef’s knife. If no one’s taken it yet, it might still be there for you to use. Ditto for 10 euros worth of plastic containers, which I took with me when I left. But for roughly 50 euros a night, I would prefer a host who supplies those necessities.
I love Monteverde, have been to Rome a half dozen times before, and don’t mind walking, so it usually didn’t bother me that I was 30-45 minutes away from Trastevere, Testaccio Market, and sites like the Colosseum, the Vatican, Piazza Navona, or Roma Termini. But if you’re coming to Rome for the first time and/or want to see a lot of the city’s main sights in a few days, this location probably isn’t for you. (Yes, the 44 and 871 bus stops are a two-minute walk from the apartment, but both buses are also slow and unreliable, both during this stay and during other stays in this same neighborhood.)

Finally, Rome was having a bit of a cold snap when I arrived the first week of March, and Alberto insisted that the heat in his apartment could only go up to 20 degrees Celsius (approximately 68 degrees Fahrenheit). Given that the controls are clearly visible, I felt kind of skeptical. Regardless, for what I was paying, I would prefer either to be able to control my own heating or to have the host supplement with a portable heater.
Alberto was patient with my having to change my plans a number of times due to Covid-related delays and rescheduling, and he was kind enough to meet me out on the street when I arrived. I hope he’ll find a way to deal with some of the issues I’ve described, and I wish him well.