Certainly it was the primary objective initially. IE was ultimately killed by the strategic decision to stop putting much resource into developing it after they'd already killed Netscape Navigator (whether that was due to complacency or fear of more antitrust action if they looked like they were trying to build on their browser monopoly). But for a long time, that just meant everybody using an outdated browser.

The bigger problem was that MS weren't all that bothered about migrating old IE users to new IE. When IE7 came out five years after IE6 it didn't work on legacy Windows and wasn't pushed in an XP update or service pack, so unlike its predecessor it peaked at less than 50% market share[1]. At that stage Firefox was far from the dominant browser but the delay had created a reason for it to exist and its market share to be non-trivial and ultimately overtake the second most popular MS browser. Overall a combination of Microsoft 6/7 and 8 still had a majority market share for a very long time, but since they were each very different browsers with large shares designers had to go to the effort of supporting multiple platforms anyway rather than just lazily optimising for latest IE. Which meant they also bothered to support Firefox etc, which meant W3C standards compliant browsers were viable alternatives for late adopters when web designers started serving 'outdated browser' warnings to IE6 users and the EU slapped MS with the Browser Choice ruling. Especially since often it was easier for end users to get a non-IE browser to work. First time I installed Firefox at work was when tech support wouldn't let me upgrade to IE7...

[1]it also wasn't the best browser of its time, unlike its predecessor was in 2001. But that didn't matter to the many people who just carried on using IE6