@Kevin Diesel
I think it helps here to understand the difference between "Loan to Cost (LTC)" and "Loan to Value (LTV)". LTC is a loan given as a percentage of how much money you have invested in the property. LTV is given as a percentage of how much the asset appraises for (the "value"), regardless of how much you personally have invested in the property.
Before the 6-12 month seasoning period is up, a lender will only give you 75-80% of your cost, even if the value is higher (or 75% LTV if it appraises for less than you spent). The idea being that they don't really want you to get all your cash back quickly, because they want you to have "skin in the game."
After 6-12 months, they will then be willing to give you a 75% LTV loan based on the higher appraised value and they stop caring about your cost. If 75% LTV of the new value is more than your entire cost, you got a "100% cash out refi."
In your scenario (100K all-in, 150K ARV), if you went to the bank 1 month after purchase and tried to get a loan, they'd only give you 75K, even if the property was worth 150K (so the loan would be 75% LTC, which in this case happens to only be 50% LTV). After 12 months, you could instead get a 75% LTV loan (112.5K), which would give you "100% cash out" (plus a little extra). But note that you're NOT getting a 100% LTV loan (they're not giving you 150K). They still always want you to have at least 25% equity left in the house.
So, to answer your question "is it smart to do a 100% cash out refi" - if you mean, "is it smart to get all your original cash back, and still have 25% equity in the property and a cash-flowing asset" then the answer is "yes." That's the basis of the BRRR strategy. You just want to make sure the property still cashflows at 75% LTV.
If you mean "is it smart to get a 100% LTV loan, assuming some bank would do so," the answer is "it depends, but usually no." 100% leverage means you have a much higher monthly payment (since you've financed a larger amount), which will make it harder to cash flow. And, you don't have any equity in the property, so if, say, the market declines and your property loses 10% of its value, you'll be under water (that is, you couldn't sell the property for enough to pay off the entire loan). There are plenty of circumstances where the numbers can still work out with a high LTV loan (e.g. some people use FHA loans with very high LTV's, or do 100% LTV seller financing, etc), but it's both riskier and makes it less likely to cash flow, so requires caution. Personally, I think smart investors have a cushion and plan for the worst, which means being careful with leverage.
Your basic math is correct - if you want to exclusively use the BRRR strategy to live off the passive income in the short term, you're probably looking at 50-100 doors in most markets. Or, wait 30 years until 10 doors are fully paid off and cash flowing 1000/m each.