This argument is flawed. There are really only two types of custom apps that you are referring to: apps that rely on ActiveX controls, and apps that use nonstandard eventing and DOM APIs, as well as bugs built into Internet Explorer.
In each case you have a problem: those who use ActiveX will eventually find a total lack of support and updates for these apps, and those apps that rely on non-standard behaviour risk getting broken in even minor updates. Not to mention there will come a time when Microsoft will completely stop supporting the browser version the app is relying on, even for security updates.
As has been pointed out by someone else, Firefox has special long term updates for corporations in restricted environments, so it's not a huge concern in terms of lots of updates being applied every few months.
In each case you have a problem: those who use ActiveX will eventually find a total lack of support and updates for these apps, and those apps that rely on non-standard behaviour risk getting broken in even minor updates. Not to mention there will come a time when Microsoft will completely stop supporting the browser version the app is relying on, even for security updates.
As has been pointed out by someone else, Firefox has special long term updates for corporations in restricted environments, so it's not a huge concern in terms of lots of updates being applied every few months.