I REALLY enjoy using my mouse with my non-dominant hand (left in this case). I originally decided to pick it up after seeing a friend of mine using the mouse on his right hand despite being a leftie which highly surprised me. For the most part, I feel that a lot of people either brush this of as being a relatively hard thing to do/learn (it's not) or just see no reason to do it (true to a degree). First of all I'd say that if you're already fully going mouseless, then switching to left-handed mouse would probably not benefit you as much. In general I'd describe left-handed mouse as being in the weird middle-ground of right-handed mouse and flat out mouseless where most people would just use mouse on their right hand and those that want to optimise their experience would just be going mouseless.
Now with that context in mind, I'm personally someone who can make do without a mouse, but still prefer the easy and less taxing solution of using a mouse when the opportunity arise, especially since navigating with mouse only requires one hand whereas navigating with keyboard may require both hands on deck. Below I'll list down the main benefit and caveat of being in the minority.
This allows for your right hand to be doing other things such as writing or even playing on your phone if you want to start "minmaxing". There have been so many instances where I'm currently writing something, but need to, say, scroll down the page or check up on new messages, so instead of dropping what I'm doing and being hit with a decrease in productivity, I can instead write AND check messages, scroll down the pages, etc at the same time. It feels pretty seamless and the fact that I don't have to make room for my mouse every time I want to use it is a plus as well.
This is truly what holding it back for me as unlike your typical right-handed mouse, there's just not much demand for left-handed variant. This not only mean that it can be hard to purchase them, but as a result they can also be rather expensive as well. You can get a typical right-handed mouse for less than $5 unlike a left-handed mouse which most of the time cost $100~ (Razer Naga Left-Handed Version), is oddly only for one size (M650L, L = Large, but it's the only sizing which offers a left-handed variant), or just gimmicky (vertical mouse). You can try coping with ambidextrous mouse (which is what I'm doing), but it doesn't really feel the same in the same vein where if you've experienced using a right-handed mouse then it can feels pretty weird to use an ambidextrous mouse. Most right-handed focused mouse for instance have the left click to be easier to press compared to the right click and would typically have side buttons located to the left of the mouse, so using an ambidextrous mouse means that these comfort and ergonomics would largely be absent in the product as it tries going for the middle-ground solution instead of appealing to a singular group.
Personally, I feel that most people think too negatively in regards to using the mouse on your non-dominant hand, so much so that they probably just ended up not bothering with it or see it as being "gimmicky". In my opinion, the learning phase is mostly fine and it is something that you can get used to rather quickly (I got used to it in a day or two). No reason not to try it out unless your workflow requires constant precise movement, so give it a go, at least for a few days. For me, the increased in work efficiency due to allowance of multi-tasking really gets to me and I couldn't have it any other way.