I assume they wrapped the wires because it made manufacturing easier. Without a socket, going directly to the transistor's legs, then wrap would be much easier than doing midair soldering.
Solder is fine. There are some photos here (link) that demonstrate good technique for how to solder this type of joint.
Here's the Sanyo 20ez schematic (link). The voltage regulator is IC601 and the power transistor is Q901. You can see them toward the bottom right corner of the schematic where the AC comes in.
Thanks again. One more silly question, this one concerning the acronym "hot". I've seen this used two ways "high output transistor" and "horizontal output transistor". Which is it, or are they the same and some people are just confusing the term? Last question...promise. :0)
Usually horizontal output transistor; it's just a description of what it does. This is the transistor that controls how the beam scans across the screen and snaps back to the start of the next line.