My observation has been that there are two problems here:
1) People, in particular business decision-makers, tend to make decisions without fully evaluating what they want.
2) IT folks tend not to negotiate a viable power structure, and allow non-technical people to make technical decisions
The solution, is, first, to sell yourself as the administrator.
By Selling yourself as an administrator, you can convince management that they're paying you to make these sorts of decisions, and that if they won't take your advice, they're spending money, that they're not benefiting from. This is a hard, risky sell, because, in a sense, you're arguing against the value of your job. An important part of this is dialog: evaluate your customer's (Boss's) need and find the best solution. Also, help him define his needs: "You need your computer to run reliably ALL the time, right? Using Firefox, help me do that for you. Using IE makes that, in some cases, virtually impossible." "They Software for the voicemail needs to be available. There are problems with the Java runtime that require maintenance, and maintenance cuts into your productive time. Is it worth it to you for me to fix a recurring problem on your time? or is it easier to use a more reliable access method?"
The second part of the solution, is to use the tools that you have
The key idea here is, you can force them into good procedure with a policy that prevents them running iexplore.exe, but that creates a political situation. that's why selling your ideas is important. With anyone lower than management, this is a great method, even with middle-management, as long as you have management support.
The last Point I'd like to make is that sometimes, just continuing to maintain a bad solution is why they've hired an IT staff, and that even though the platform has lots of issues, If the management wants to use that platform, and it creates a job for you to do, do that job, It's why they hired you. If there's a problem with software running on that platform, do your best to discuss it with the vendor, and involve management in the discussion as neccesary, and allow them to share your frustration on an experiential level; they'll have a better point of reference for understanding your advice in the future.