API = Standardisation (to a much larger extent than text files)
Having spent a couple of years developing an application that a particular client wanted to interact with MYOB I would seriously recommend a GL with API.
Text file import/ export is an horrendous way to run a company.
(IF) you ever need any customisation of the product/module the first thing any developer is going to do is build some kind of API if you dont already have one. Then 6 months later, she is unfortunately killed in a car accident... and you need some more customisation. So the next developer looks at the scratch of an API started by the first and then modifies/appends to that for the purpose at hand... and so on.. and before long you have a frankenstein on your hands.... because as you say you dont develop in house and whose to say any of these developers are experts in the GL module anyway. So they start creating their own API's according to what they think is the GL module, not neccessarily what it actually is.
Whereas a product with a prebuilt API is straight form the horses mouth. The people who built the GL module are saying this is how you should interact with our product programmatically. Then you can go out and get a developer who actually already knows the API.... from that last job they did. i.e. they dont have to learn your company's frankenstein first.
Also with a pre built API, add on modules/upgrades etc from 3rd party vendors become more feasible. Again because the GL's API is standardised and known outside of your company and therefore represents a market opportunity to hungry developers.
Security: With an API you can more securely communicate with your GL. It's much harder to hack a systems process memory to mess with GL API based imports/exports, than it is to open and modify a bunch of text files sitting in some folder on the file system.
Your argument seems to be we dont need programmatic access to the product and we never will, well good luck with that. ;)
If you've recently under taken a full strategic review of how IT is used in your company and can honestly say they you will never need to modify either how you get data into your GL and how you shape data coming out of your GL then go ahead and by pass the requirement for a new GL module to have an API.
That said the future is the great unknown. I personally would NEVER recommend a GL module without an API.... simply because I know whats out there.... and no accounting package that I'd be looking at for our customers (SME's) going forward is without an API.... especially given the uptake on cloud computing.