This is coming from a rather outside game mechanics position, but having both spells and swordplay skills sounds more like the same kind of diversification someone would have taking longbow training and also having training in melee combat. (Longbow training IRL took a lot of years to get good at).
The main advantage is that the warrior in question can enhance their own weapon and armor to bypass magical defenses. They aren't going to waste their time increasing the destructive force of a single strike unless they are doing something like trying to break through a gate during a siege, because it would take too much time to both use the incantation and then actually swing the sword.
Mobility is the second potential use of magic that might be useful. But again, the benefit has to outweigh the extra cost in time to incant. Such a character would probably be using magic to reduce the burden of long forced marches across terrain instead of trying to use it readily on the field while in active engagement.
Now a tradition that doesn't use incantations but does something like channeling magic in less aggressive ways could work. Like you have charges that are prepared in the morning where the individual is actually doing the incantations, and the warrior would then expend the charges during combat or over the course of the day. This would pair well with enchanting a weapon in the morning so that it can bypass magic defenses.