I can absolutely say that "I couldn't answer the question first" is not a motive people had for closing questions. That would have been abusive and definitely something that moderators would follow up on and deal with to whatever tiny extent it happened.

I can say extremely confidently from years of experience that the people who were always "trying to be the first to answer your question" were, overwhelmingly, the ones trying hardest not to let anyone ever close anything, even harder than the most aggrieved newbies asking questions and not caring about the underlying community. Nobody sits around answering multiple questions a day for years on end, purely on intrinsic motivation. I joined in late 2010 and posted answers all the way until mid-2023, but fully half of those were before the end of 2012. There are reasons for that. Meanwhile, there are people with reputation scores in the seven digits, even though the site awards no further privileges past 25,000. The obvious conclusion is that we're primarily talking about people primarily motivated by Number Go Up, and closing questions is an impediment to Number Go Up, so it must be prevented at all costs.

Questions get closed for the reasons that are listed in the interface for closing questions, which are also described in the Help Center and also explained in detail on meta (https://meta.stackoverflow.com/questions/417476). When questions don't meet the expected standards, it's important to close them as quickly as possible; because when people answer questions that should be closed, they are actively making the site worse (https://meta.stackoverflow.com/questions/429808). And since there will always be people around who are motivated by Number Go Up, there was value in preempting them.

Really the system was poorly designed. The Staging Ground was the one shining beacon of hope, because it inherently prevented answers by default, providing only a comment thread with the explicit purpose of fixing issues with the question so that it could meet site standards.