If you're very lucky you can wind up with the best of both worlds.
I've been on an organized three week trip to Peru, which was nothing short of mind blowing.
The thing is that my sister in law is Peruvian, owns a house in Lima, worked at the presidents palace (which we were able to visit on short notice) and has a lot of friends and family around the country.
So while she had some of things organized (you partially must. You can't spontaneously visit Machu Pichu [which was a bit of a disappointment, but I digress]). But she had those parts, which needed to be pre-planned organized by local travel agents and tour operators. Obviously, knowing the language, the people and the place was extremely valuable for that.
So, despite that it was essentially a "package tour" it felt like totally individualized travel.
While some of the elements certainly can be booked as part of a packaged tour I don't think it could have been done with such quality and insight without the local knowledge.
Another thing, which I found can be immensly valuable is hiring a local guide. A guide and car in Siem Reap (Cambodia) hit me with about 30$ a day (& tip). Sure, you can visit Angkor Wat by booking a tuk tuk, buy a guide book and head off on you own. But you'll have to make sense of a temple installation scattered around 400 km/2 on your own.
Having a guide on my side opens doors to places, which I would never have been able to do on my own. Let alone of getting all the background on country, poeple and (yes) politics.
Travel can broaden the mind, but only if you let it, and most of the ways in which it does are through giving you unexpected things, good or bad. The more tightly you plan, or buy a package in order to remove uncertainty, the less serendipity you get. You can't order a surprise for yourself.
Given this philosophy, I felt bad about allowing a tour company to plan my South American trip rather than booking dozens of transfers myself, but in the end serendipity worked anyway and somehow we ended up with two of us on an itinerary clearly designed for larger groups. Speeding across Lake Titicaca on a catamaran to ourselves remains a peak experience. Later on we got to Machu Picchu, which really is reaching critical levels of self-destructive tourism: https://www.theguardian.com/cities/2019/may/15/archaeologist...
(There is also something to be said for both straightforward hedonism and the "precision relaxation" of people who go to the same hotel for 20 years to order the same drinks, but neither of those really needs or deserves to be allowed to ruin a local community or natural wonder in order to make it happen.)