I am not following what the OP expected UA to do. All the seat assignments were assigned, thats why there was no seat assignment available. This happens regardless of what fare you purchase. So would UA be expected to bump someone out of their seat assignment? That would be ridiculous.
Yes, this was considered a close-in purchase as the seats were all assigned at the time he/she purchased. It really is a first come first served situation with seat assignments.
This happens to every airline, so taking that ticket to another carrier will not solve the problem. The reason for this, is that airlines oversell planes to maximize revenue. Even if the plane was not oversold, and sold close to capacity, not all seats (156 in this case) are available for preassignment - exit rows and not being eligible for E+ will restrict the OP from being able to assign a seat. Again, this would have happened regardless of the fare he/she was on. The airlines solve this by assigning the seat at the gate. Happened to most of us at some point in time, and we just accept that seat and get on board. Its not that big of a deal to wait that long to most, but it apparently is to the OP and I respect that. Its just one of those things that happens while traveling.