In the last gen mandatory HDD installs were the exception, not the rule.
Most Xbox 360 and PS3 games had to load most of the data from the optical disc (DVD or Blu-ray):
The Xbox 360 had a 12x DVD drive, so sequential max. speed 15.8 MB/s with abysmal seeking speeds compared to 5400 rpm HDD.
The PS3 had a 2x Blu-ray drive, so sequential max. speed 8.6 MB/s with abysmal seeking speeds compared to 5400 rpm HDD.
Last gen already relied on HDD, installing bits and pieces or using the HDD as cache. Plus last gen actually had tricks to use both HDD and optical drive together. The digital version of Halo Reach actually performed worse with only the HDD to run from instead of using both pathways.
So actually we went a bit backwards this gen in general I/O since everything is installed on HDD now, no more benefits from a secondary source.
Sorry, but you are wrong. (Or I'm dreaming I had to wait 10 minutes between MGS4 chapters to install the next part to HDD)
Most Xbox 360 games of the first years worked without any HDD. A few later games needed a small HDD for some caching and for patches, but most of the data still was loaded directly from the DVD.
Most PS3 games only needed a small part of the HDD for some caching (usually as mandatory installs of tiny fractions of the game) and some patches, but most of the data still was loaded directly from the Blu-ray.
Xbox 360 Core and Xbox 360 Arcade existed, the PS3 Superslim with 12 GB existed.