> And when you decide it's no longer worth it, you might even have issues getting back in to get your stuff...

Do they refuse tourist visas for someone who recently had an immigrant visa?

They sure do. US law presupposes that a tourist is secretly planning to stay in the US, and must demonstrate otherwise to the satisfaction of the assessor. There are a number of factors assessed, including things like ties to the applicant's home country - an existing job, ownership of property, family demands; basically, clearly having a life in that country that the applicant wants and needs to get back to.

Someone applying for a tourist visa, who recently had an immigration renewal denied, who has no life to get back to in their country of origin (because they built a life in the US) but clearly has a life in the US (owns property in the US, has family in the US, has work ties -maybe even still has a job in the US); that applicant is an enhanced overstayer risk and this increases the chances of being denied a tourist visa.