The variety was certainly different compared to now. Now we have a greater delineation in lower-budget games compared to the 6th gen with digital storefronts. You had greater number of third-party physically published games, sure, and that had its own a benefits. Concepts like DLC were sold in a multitude of ways (expansions, map disks and yes, downloadable content). Most generations have lessons and experiences to offer. I think indies/digital-storefronts probably leads to more games available now due to accessibility, but I'm not like checking numbers published or anything. The games are there, just in different places.
To the OPs point, I do agree that the 6th gen was a particularly interesting time in the business of gaming. It's interesting this comes up as my wife and I were talking about something somewhat related - the transformation of technology over time due to advancing technology. Those a little older will see just how much concepts have evolved from halcyon days. The 6th generation was effectively the developmental peak of "games as a finished product" if you will, versus the transition to "games as a service" even if early attempts like Halo 3 and COD Elite subscriptions fizzled. In concept of the experience a 6th gen or older game provided was more or less the same: a siloed experience that will (more likely than not) never change. It's ad-hoc in a way. Your exposure to what the world was doing with that game was tied to your world view, effectively.
In hindsight, the revolution of the 7th gen wasn't HD development and the increase in costs that entailed. Truly revolutionary ideas become general concepts, versus being tied to the form; anyone who played games in the 7th gen would point to widespread online networking being the true change. A connection to every console brought forth so many possibilities that Sony/MS/Nintendo could rely on. A living online storefront. Updates for games, updates for the console itself. Online communication, including online gaming itself. Of course all these aspects dabbled in gaming through the 90s, especially in the PC space. The simplest way of explaining it was prior to the 7th gen, we were told by the console manufacturers were were going online at your yearly E3/TGS/Gamescom/etc. In the 7th gen, we were actually online, finally. It was far more common and accessible versus the past. On top of increased online connectivity leading to a rise in things adjacent to games. Streaming, content creation, Discord, specialist forums, esports and competitive gaming being more accessible, etc.
The Wii is a bit transitionary, in my eyes, which speaks to Nintendo's perspective about game development online connectivity at the time. Of course, Virtual Console and WiiWare demonstrated Nintendo were well aware of the ability of delivering content through the internet. Yet they made game patching a rarity due to Wii peculiarities, which might have been driven by Nintendo's stance on delaying and pushing out finished products. On a broader scale, it almost makes sense they marched to their own beat given Nintendo's then-current "blue ocean" approach.
The conveniences of online networking has changed games and I agree with them in that sense. It's not all bad though it's not exactly taking a stand against The Man to say I want games to at least come out more feature complete and on reasonable timelines versus crunched out for mastering and then crunch again for a day 1 patch. I'm not a fan of introducing more luck-based gambling or gatcha aspects to games I've already paid for. On top of incessant microtransactions. Unfortunately many are fine with this and this is where parts of the industry are going.
This is not to say the 6th generation was without similar morally dubious issues. Halo 2's 2003 demo being a complete farce. CGI ads and trailers. Multiplatform games not being shown at all before release and coming out poorly on Xbox and especially GameCube are issues. And a mastered, un-updatable game is not necessarily a bug free one. Tons of games were still released broken or unoptimized, either due to interest, time or skill. There's a reason "licenced game" was a scourge.
Looking back it was certainly an interesting time. PS2 is still the world's best selling console. It achieved that for good reason through the years of consistent quality and how many landmark titles were released for it. The launch was incredible and unlike anything ever seen in games to that point. As a business model, it did represent the end of an era, one that did truly affect the games themselves, though I think it's more to do with how games evolved versus what games were.