Are there benefits in targeting local companies to use my SaaS product?

I'm developing a software as a service product due to a problem I was experiencing when emailing clients. Without going into too much detail about it; it's a product that would be aimed towards companies who send lots of the same emails. ie. a recruitment company that sends out a lot of "cold-call" style emails to prospective employees, or a law firm that sends a lot of legal contracts that are generally in the same format.

Now I want to contact potential users of the software to try it out for free while it's in BETA. It would be fairly easy for me to compile a list of possible business types of who would use it and then outsource the collection of email addresses for me to send information about the product to.

I was thinking that it might be better to do this on a local scale. ie contact companies in my city specifically. I would maybe note that I live in the same city as them in my enquiry.

Are there any reasons I shouldn't do this?

As a Beta, it would be worthwhile getting views of those in other countries etc so restricting it to one area might not be truly representative of feedback when you go live - for example, different countries have different rules/laws and cultures and it would be remiss not to get feedback from as varied as possible audience.

That doesn't mean you shouldn't get views from local companies but I wouldn't only get from them.

Even for a SaaS product that's theoretically available to anyone in the world, the general advice for B2B products is to start with a super small niche, get a few customers in the door, and then learn from them as you expand to broader markets.

What it really comes down to is that you need to have an initial customer base so that you can start learning about their needs. Running a beta is a great idea because then you have more latitude to make big changes, and you have more of an excuse when things inevitably break.

From a learning perspective, where these customers are geographically located makes almost no difference. But from a marketing perspective, acquiring new customers locally is often much easier than trying to canvas the entire internet.

Going to some local meetups and talking to local businesses is a much easier way to acquire your first customers than trying to rank #1 for "cold email service" on Google. Pound the pavement and talk to people in your area about your product. You'll probably build more of a rapport with your early customers this way because of the face time.

Overall, I'd say that it's almost better to start local and then try to expand across the internet.