Given your stated level of spending, it doesn't seen that there is a compelling benefit to holding multiple cards.
Some high spenders can get away with it, because hitting certain levels on several cards is worthwhile to get the bonuses in each category, and also depending on their needs.
For example, the Delta Amex is nice because of the free baggage limit, and basically pays for itself if you take 4 flights that you would otherwise check a bag. Much faster if you add more travelers. At ~20k annual spend, few of these will offer anything very significant.
Check out Nerdwallet to get some more detailed info.
A handful will avg out to ~2% redemption rewards (citi double - cash back, barclay world - travel rewards), while some also have certain drawbacks which you'll have to weigh separately like annual fees, foreign transaction fees, etc.
Personally, I prefer simplicity and have gone through a handful of cards (maybe 5) in the past 5 years, and settled in late 2014 on the capital one quicksilver. 1.5% cash back on everything and no foreign fees means I am a happy camper. Automatic redemption in $25 increments means I don't really have to think much about it.
I probably spend in the 10-15k annual range, so perhaps if one day when I have a family and that increases to 20+ then there may be benefits in going for point and travel bonuses on some of the cards, but again that does require some level of effort.
All depends on which features are important to you, and how much (if any) effort you want to put into it.