Are integrated amps technically better than separates?

NO not this week.

I'm thinking the integrated could actually be an improvement over separates due to being a more "direct" connection. Taking away the flexibility factor of separates, is my line of thinking correct?

It is. To match the performance of a good integrated amp requires a very good and high quality (read: expensive) interconnect between the pre amp and amp. To say nothing of another quality power cord. Add in the cost of the extra PC and IC and its still possible to get better performance, but only by spending vastly more money. 

If you're like me then and you care about performance per dollar the integrated amp really is the only way to go.
 https://systems.audiogon.com/systems/8367

One reason why most top-end preamps have separate power supplies.

Of course, nothing sells like excess.

... and over the top power supplies wreak havoc on low level preamp signals and negate any benefit from "direct" connections’. One reason why most top-end preamps have separate power supplies.

Like anything, specifics matter.

Could they be? Yes, certainly. The issues of DC coupling and impedance matching of each stage to the other vanish, not to mention the need for another set of interconnects, and the possible issues with proper connections at each of those points.

One of the other places where separate costs don’t really add up for the consumer is in the cost of the cases. Separates require more casework and associated assembly times, so you pay for that without any direct value add.

I am very happy to have turned into a Luxman integrated owner. It’s solved a number of issues with space and connectivity as well as improved the overall sound quality vs. the previous set up.

At the total price point I am at, I would have a very difficult time doing better with separates. Now, if I were to spend 4x as much with separates, that’s another story. :)

In a word: No

Once you get past a certain level it becomes all about power supplies.  It's easier to fit over the top power supplies in separate components.