I'm a Panther solo, and I'll generally go ahead and deliver early if I can, for the above mentioned reasons. The quicker you deliver, the quicker you can get your next load, etc. Also, often the consignee (and customer, if different) is very appreciative of the speedy service. On the other hand, being a solo, on long trips I won't sacrifice safety in order to deliver early. If I have plenty of extra time to make the delivery, I'll take my time in getting there, stop off for a nap when I need it, etc. And there are cases where an early delivery is actually not wanted.
I just came off a 1307 mile run, Laredo to SC. Had tons of extra time to make the delivery. 1630 Monday pickup with an 0700 Wednesday delivery, 38 1/2 hours. At 47 MPH it's a 29 hour run, but that would have made the delivery time at 2200 on Tuesday, when shipping and receiving was closed, so they scheduled it for the next morning. In real world driving it's about 21 hours, which meant if I had driven it straight through I could have made the delivery the next afternoon, but a solo driving 21 hours straight in insane, and it would have been closer to 24 hours because Atlanta construction sits in wait near the end of the tip, and Atlanta at noon, or anytime during the day, is not pleasant under the best of circumstances.
So, I took my time. Slept about 7-8 hours in Houston Monday night, drove a long way Tuesday, then slept a little while in Montgomery, trying to time it by hitting Atlanta between 1-2 AM. I hit Atlanta at 0130, then drove on up to the delivery. I didn't expect them to be open at 0510, but they had just opened at 0500, so I made the delivery 2 hours early.
In this case, as is the case more often than you might think, if I had made the delivery the previous afternoon or evening, the person who was expecting the delivery would not have been there and the freight may have gotten misplaced or lost at the consignee. I mentioned that I could have delivered it the previous day, and wondered if that would have been OK. She (cons) said that she was glad that I didn't, because this was a JIT thing and if it had come in early there would have almost certainly been a delay on the line while they had to search for it in receiving. By making the delivery on-time Wednesday morning, she was able to take it directly to where they would be needing it in a few hours.
So, it depends on the situation. Generally I'll deliver early, but after a while you kind of get to know which ones can and cannot, and which ones should and should not, be delivered early. In almost all cases, though, my goal is to never arrive any later than 1-2 hours before the scheduled delivery time, even to places that I know for sure aren't open that early. I'd much rather sit for an hour or two at delivery than be late due to unexpected construction or something along the way.