Is taking out a loan for a down-payment on a house a good idea?

I’m not sure if this is common, uncommon, or just completely dumb to try and do. But feedback and input would be greatly appreciated.

I make about $38,000/year after insurance, taxes, 401k, etc. This is my take home pay.

I have about $21,000 in my savings and checking combined. My credit card is always paid down and has a $7,000 limit.

I spoke with a mortgage lender rep a few months ago to see if I could start the process to get pre qualified for a home loan. After the conversation, I felt very defeated because there were a lot more closing fees, inspection fees, insurance, etc. that I did not know went into buying a home.

If I have to find a place to rent for another year or two, that will be $1,000+ a month, and will leave me with only $500-600 that I can put away into savings for a house down-payment. Starting next year – after student debt relief kicks in – I will still have an outstanding balance and be paying around $300/month on those to aggressively pay it down (and increase my payments each year as I make more money).

I just feel impatient because many people have pointed out to me that their mortgage payments are much less than it costs to rent every month. Should I be more patient and wait for a big promotion to pull the trigger on a house hunt?

Also I suppose a possible pro to paying that much in rent would be not having to pay to fix things around the house if it breaks. But I think it would be awesome to own a house and start owning some equity that will pay myself back later on.

Thoughts? Opinions? Tips?

To clarify/tl;dr: is it a smart or dumb move to take out a loan or rack up credit card debt to afford a down-payment and closing fees, in addition/separate to taking on a mortgage loan?