I was born in 1976, I was enjoying Sega arcade ports throughout gaming and it was an amazing feeling to be able to play almost arcade perfect arcade games on the Saturn (I was BIG into arcades at that time too). It just sucked that Sega was wanting $50 for these ports, I understand development is not cheap and people need to be paid but fans voted with their dollars and in cases like this, at least in my circle of friends, PlayStation won almost every time.
I would bring up Daytona (my apologies on getting the name wrong, I am going off memory here) and my friends would point out Ridge Racer. Virtua Fighter 1 and 2 were countered by Tekken. Sky Target was countered with Warhawk (not an arcade port but still even a blind man could see how amazing that was back then).
Adding extras, advertising those extras, would have done so much for Sega but they were horrible at this. They peaked with their advertising with the Sega Genesis and the "Welcome to the Next Level" campaign as it was all downhill after that.
Another area they completely and utterly failed their fanbase was no 2D or 2.5D Sonic on Saturn. Instead we got Clockwork Knight 1 and 2 (mags of the time made sure to point out this was ONE game in Japan) and Bug 1 and 2 (Too). Astal gets a pass here as it was simply beautiful back then.
Sega came into the 32-Bit race ahead of schedule and fans like me thought they did this because they had a new Streets of Rage, Comix Zone, X-Men, Sonic, Phantasy Star, etc ready to go and would drop them closer to the launch of PlayStation six months or so later. Sadly, history shows us, this was not the case and Sega was traversing rough waters with no manning the helm of the ship.
Virtua Fighter Remix was what the original release should have been on Saturn with "arcade visuals" being an option, even make the Remix an unlockable if need be.
I would love to see Sega do a Super Scaler (Space Harrier, Thunder Blade, Super Hang-On, etc) collection even if they only improved the frame rate. The value of a collection would be in the number of games for the price rather than added content or unlockables. Sadly, back in the Saturn days, Sega passed on doing just this with their Sega Ages series and instead we had Working Designs step in to release one with three games on it (After Burner was one, I remember definitely being included).
The Dreamcast had a good amount of 3rd party support, Capcom were kicking up a lot of dust with their support for Sega's last console. Sadly, it was either ahead of its time or was the victim of how Sega ended the Saturn (which did cause EA to snub the DC).
The Dreamcast was a nice farewell to hardware manufacturing for Sega. It is sad but looking back on it, it appears that is exactly what it was meant to be. Sega poured development money into their releases on this console and pushed hard (if only they pushed this hard on the Saturn) but as you mentioned, the PS2 was just too strong an opponent to take on. Sony did so much right by gamers with the 32-Bit generation that it would be near impossible to crack that support Sony had before they even released the next PlayStation console.