If you're really looking for an excuse to play through the classic Sonic games again, Origins does scratch that itch, but it's not without some issues that may hamper the experience.

• The physics and game logic have a few bugs that weren't in the originals. For one, Tails doesn't despawn/respawn properly in Sonic 2, meaning sometimes you can hear him repeatedly jumping offscreen trying to reach you.
  
• The missing Sonic 3 music is a big loss; the replacement tracks just aren't as good.
  
• Biggest issue: The "Classic Mode" isn't actually Classic Mode, it's just Anniversary Mode cropped back to a 4:3 aspect ratio and with Lives re-enabled. You can tell because those same physics bugs (which weren't in the original versions of the games) are present, and also because you can Spin Dash in Sonic 1 Classic Mode, when you couldn't in the original.
  
• Sega removing the Sonic games from the SEGA Mega Drive and Genesis Classics collection is extra scummy because of the above. If you want to play the actual original versions and you didn't already own them, it'll either take a ROM or some Workshop chicanery.
  
• Potential itch notwithstanding, $40 is too expensive for this. The only significant addition beyond the games is Mission Mode which, while fun, is also too easy for the most part, save for a couple Missions in the higher ranks.

That being said, these issues are ultimately minor compared to everything else. The games still play well for the most part, and the 16:9 gameplay of Anniversary Mode is a nice change of pace compared to having played the games in their original forms several times already.