When I rode on the now gone Madison Velodrome in the Detroit area in the 70's, you were required to use tied and soldered wheels. I dutifully did so with one pair of track wheels comprised of Fiamme Red Label Rims, Robergel Sport spokes (3x), and Nuovo Record Hubs. The 50 degree turn banking on the approximately 150 meter track put some unusual and severe compressive loads on the wheels.
I'm not sure what soldering does other than to make the joint more solid but tying the the spokes strengthens the wheel against collapse. Shortening the spokes "free length" increases the strength of the wheel. In a normal wheel the free length is from the hub flange hole to the rim hole. The tied and soldered wheel adds an end point at the spoke crossing and effectively shortens the spoke. Given a spoke of the same diameter, it is more difficult to buckle a short spoke than a long spoke. Fixing the free end of the spoke to the crossing point reduces the likelihood of spoke bucking. This description is a simplification of elementary column structure principals. A spoke in compression is a column.
For those of you in the Bay Area during the 1989 Earthquake, the Cypress viaduct was a real example of buckling columns. In that situation the earthquake added forces greater than normal design parameters causing the steel reinforcement to buckle, shattering the concrete around the steel and causing the collapse of the bridge deck(s), killing 50 people. The remedy for older structures that survived that event was to install a steel jacket around the columns to contain the concrete and preserve the column compressive strength.
I can vouch for the unusual compressive loads. With the banking of 50 degrees and a gear ratio restriction of 84 inches, the range of speed on that track was between approximately 18 mph and 32 mph. Above 20 mph you wanted to lock your elbows in the turns so that your chin didn't hit your stem. I'm sure the wheels were going into a bit more oval shape at the same time.
Replacing rims is easier, with a tied a soldered wheel. Tied on soldered wheels on the road is not particularly advantageous. It does make the wheel more rigid. If you hit a pot hole the rim will take more of the impact than usual and the likelihood of rim failure increases. The wire and solder also adds weight to the wheel.
Todd Teachout
Hercules, CA