It sounds to me like you do have good reasons but that you're just second guessing if they're good reasons!
I think that especially if you have experiences that co-relate to the work done in commercial law and the skills needed to be a commercial lawyer, they are most definitely going to be strong reasons for applying.
On the commercial insight point, you don't necessarily need something that demonstrates that but it could be beneficial. This doesn't mean you need something like work experience at a bank or at a huge company, but it can just be smaller things. Maybe you worked in retail and enjoyed learning the different strategies that business use to generate revenue/make up for losses. Or maybe you attended a presentation at a firm on a specific deal and enjoyed hearing about the different commercial considerations that went into it. The reality of applying for a graduate job straight out of uni is that many people don't actually know for sure what it takes, and if they have the experience for what it takes. The best thing that you can do is be authentic about your reasons so that they come across as convincing as possible in your application. As long as you're really explaining why those experiences and skills make commercial law the best career for you instead of just using generic words like "interesting", "exciting" etc. you're more than fine.
The only other general bit of advice I have is that when I was attending a series of workshops with Dentons as part of the AS programme, something grad rec said is make sure that when writing apps to strike a balance between an interest in the legal of side of things and and interest in the commercial side of things. So I generally structured my answers to explain why I enjoyed the skills involved with working with both black letter law and commercial/business issues.