Need for locking out suspension.
 

I am 70 years old with back problems. I bought a Cannondale Super with full suspension and also have a Trek X-Caliber with front suspension.
I have a lot of rough streets in my neighborhood and I really like the suspension.
I have read that most riders lockout their suspension on smooth roads.
I guess it's a matter of personal preference but is there a reason for this?

Yes. The suspension absorbs energy which would otherwise move you forward. So if you don't need it, it just slows you down.

It is much more noticable when trying to go up hill,,,,, I also like suspension, unless going uphill!

Loose grip on the bars helps with non suspension bikes

air oil shock forks you can stiffen/soften them with more/less PSI of air.

There are different factors involved, different types of suspension, etc. It depends on how smooth you are and the surface you are riding on. If you tend to stomp the pedals the suspension will "bob" as you go and if you spin smoothly you will bob less, or not at all.
When climbing or even just riding along on a rough surface, the suspension is an advantage. I've only used suspension on a mountain bike but I've never felt the need to lock it out. There are some designs which bob more than others, and the longer travel systems would probably be the greater offenders.
Whether the movement of the suspension (on a smooth surface) bothers you is something only you can decide.

The only bikes I have with suspension are only ridden offroad. They have lockout settings on the suspension, but I never have a need to use it.

What is your objective?

Since you are riding a full suspension mountain bike on the streets I'm guessing that you value smoothing out the bumps over the last increment of high speed performance. We all do that to some degree, even the pros use different bikes for cobblestone race routes.

Lower pressure in an air fork or shock lowers the sag height and increases the spring rate, neither of which improves the ride.

Ok, never needed one ..
Bent elbows and knees were sufficient for suspension .. Though I now have a suspension seatpost on a bike.