Speaking from experience, it's much harder to try and communicate with brokers (or indeed any organisation) through web interfaces than through provided API's.
So for example to scrape the positions from IB activity reports is much more involved than making a single API call. Also it's not a supported method. If a broker makes a slight change to their web interface you are screwed. I speak from bitter experience of writing data scrapers - days writing ugly code that worked for about a month before a website upgrade killed it. If they make a slight change to their API they will ensure it's kept backwardly compatible.
Trying to submit orders via the webtrader will be even harder. Quite apart from the fact that IB don't want you to do this, they want you to use the API, and will make it very very hard to do it any other way.
If you change brokers, it will be a lot quicker to write new API code (assuming it's properly isolated) than to write new web scrapers and order submitters.
Seriously, this is insane.
GAT
Exactly. If it all falls apart you'd know early on and probably have time to fix things but assume some part of the order page is slightly changed and suddenly your code tries to close a position but the regex (assuming you'd use regex) doesn't match anymore, you're screwed.
API does not change that often and is much more stable.