To me there's no substitute for keeping the floor clean. We don't seal grout. When it needs to be cleaned, we clean it (with Barkeeper's Friend). Sure, it's a chore, but you should be keeping your floor clean no matter what it is.

Epoxy grout. (I have no personal experience with it. I just read a lot.)

Epoxy grout is amazing to keep clean...it just doesn't get dirty - or at least it's carefree in my shower. I couldn't vouch for how it responds to ground in dirt on a dry floor. But, of course, that would involve regrouting your whole floor.

I don't think dirty grout on floors is any indication of someone's cleaning habits. If you have dogs or people wearing their shoes inside, dirt's going to get ground in before you vacuum, sweep, mop, etc.

I have tile counters and found the best way to clean them is with a handheld steam cleaner. So if your sealers aren't doing the job, maybe steam cleaning once in a while will make cleaning less of a chore.

13 years ago I cleaned our bathrooms with grout cleaner and a thin stiff brush, on my hands and knees. Don’t remember what cleaner, but when I had it as clean as I could I used a white grout pen. Worked wonders!

Grout does get stained and deteriorated over a period of time if not sealed properly. Some cleaners only offer superficial cleaning assistance, but as grout is porous, you need a penetrating cleaner for a thoroughly sanitized surface. If you find your grout dirty and stained, you can use a deep-soaking penetrating cleaner that enters inside the porous grout and eliminates mold and stains from within. I faced a similar problem in my bathroom. I used Imperia Deep Clean to clean my grout properly. I also found my grout missing in some places and to restore the grout, I used an epoxy resin filler - Sentura to refill in the missing areas. Although you get a clean surface after using Imperia, you cannot guarantee that staining will not occur again, and so it is important to seal the grout after cleaning.