In theory, that is all true. In reality:
- Unless you are really good at soldering and prepare everything just right, you will end up with a high-resistance connection. That may be OK, or it may overheat. That is particularly a concern with 10 AWG wire. Why? Because at least with 14 AWG (15A) or 12 AWG (20A) circuits you might really be using just a couple Amps and not have too much to worry about. But nobody uses 10 AWG unless they are really expect to use at least 16A (80% of 20A) continuously. In fact, typical 10 AWG wire on 30A breaker is for a 19A - 24A continuous load such as a water heater. Even just a little extra resistance will create a lot of heat. Not a good idea to try that.
- Breakers and other devices (e.g., receptacles) are normally designed to handle stranded wire without a problem. So this is a lot of work for no real benefit.
- If you happen to have a device that can only use solid wire, just get an appropriate UL or ETL listed wire nut. For example, most Ideal brand wire nuts and In-Sure Push-In wire connectors list exactly what size solid and stranded wires they can use. For example, an In-Sure Blue is rated for 30A, #14 - #10 solid and #12 - #10 stranded. The Twister Wire Connectors specifically mention "solid-to-stranded" and 341 Tan should work fine. Many other options, and that is without even looking at other brands of connectors.
So if you have any concerns about stranded, just get a short piece of solid wire, same size, same type (copper presumably - don't mix copper and aluminum unless you absolutely must), same color family (e.g., black or red or blue or orange or yellow for hot, white for neutral) and a good connector and you're all set. Leave the soldering iron for low-voltage projects.