I think you have misunderstood the advise you were given.

When you are advised to make sure your research interests align with those of some of the people working at the place you are applying to, people typically expect you to do the work yourself, not delegate it to random faculty members. If I received an email asking me what my research interests are, I'd either bin your email or, if I'm feeling generous, redirect you to my easy to find personal webpage where I've listed my research interests in great detail.

What you should do is go to the webpage of the institute/school/centre/unit/whatever you are applying to, and look through their staff directory. For each faculty member, there will often be a short summary of their research interests, and/or a link to their personal page, and/or recent/important publications (publications can be found in many other places as well, e.g. Google Scholar). If you cannot figure out the research interests of a faculty member using any of this information, perhaps graduate studies are not for you.

Or if that's too tedious for you, you can always look at research groups first to narrow down the list of faculty members. In this case, go to the webpage of each research group affiliated with the place you are applying to, and there should be a summary of the group's interests/goals somewhere there. If that information is not enough for your needs, but so far you think that group may be a match, go through the staff directory of the group and check the research interests of each group member. And if you want to know the specific things the group is working on, check the group publications.

So, contacting faculty for research proposals is inevitable, but completely unnecessary for research statements.

I think you have misunderstood the advice you were given.

When you are advised to make sure your research interests align with those of some of the people working at the place you are applying to, people typically expect you to do the work yourself, not delegate it to random faculty members. If I received an email asking me what my research interests are, I'd either bin your email or, if I'm feeling generous, redirect you to my easy to find personal webpage where I've listed my research interests in great detail.

What you should do is go to the webpage of the institute/school/centre/unit/whatever you are applying to, and look through their staff directory. For each faculty member, there will often be a short summary of their research interests, and/or a link to their personal page, and/or recent/important publications (publications can be found in many other places as well, e.g. Google Scholar). If you cannot figure out the research interests of a faculty member using any of this information, perhaps graduate studies are not for you.

Or if that's too tedious for you, you can always look at research groups first to narrow down the list of faculty members. In this case, go to the webpage of each research group affiliated with the place you are applying to, and there should be a summary of the group's interests/goals somewhere there. If that information is not enough for your needs, but so far you think that group may be a match, go through the staff directory of the group and check the research interests of each group member. And if you want to know the specific things the group is working on, check the group publications.

So, contacting faculty for research proposals is inevitable, but completely unnecessary for research statements.