Check the newer Bitmains miner which is the Hydro s19 pro+ according to ASICminer value you can earn 26$ daily the ROI would be around 1 year and it also depends on the price of Bitcoin. The difficulty increases from time to time so it depends on the price of Bitcoin if you can get less ROI reach or ROI more than 1yr.
You can find other ASIC miners from asicminervalue.com if you are looking for a higher profit with less ROI but don't buy on their 3rd party sellers listed there only buy directly from the manufacturer or verified distributors.
Did you exclude the electricity price from your number? As per mining calculator, with s19 pro and electricity price like 0,06$ per KWh (which is a low price) you will earn 17,5$ daily. So even with low electricity price it requires 1,5 years of non-stop work (may be longer if you consider halving) of s19 pro that costs 9,5$k + probably some other expenses.
So generally, OP is right. According to mining calculators, purchase of asic miner would pay off in about 2 years depending on your electricity price.
Right now, crypto mining is not a free money. For single individuals mining profitability depends on upcoming BTC price. If it rallies anytime soon then your purchase pays off faster.