Firstly, I'm going to do what you said and analyze your question taking your entire family's finances into account. That means giving you an answer that maximizes your family's total wealth rather then just your own. If instead of that your question really was, should I let my parents buy me a house and live rent free, then obviously you should do that (assuming your parents can afford it and you aren't taking advantage people who need to be saving for retirement and not wasting it on a 25 y/o who should be able to support him / herself).
This is really an easy question assuming you are willing to listen to math. Goto the new york times rent vs buy calculator and plug in the numbers:
Firstly, if you do what you say you want to do buy the house all cash and live there for 4 years, it would be the equivalent of paying 1151 / month in rent once you factor in transaction costs, taxes, opportunity costs, etc. Take a look at the calculator, it's very detailed.
This is why you should never buy houses all cash (unless its a negotiating tactic in a hot market, and even then you should refi after). Mortgage rates are super low right now, all that money sitting in the house is appreciating at maybe the rate of inflation (assuming the house value isn't going down which it can very easily do if you don't maintain it, another cost you need to factor in). Instead, you could be invested in the stock market getting 8%, the lost opportunity cost there is huge.
I'm not even considering your suggestion that you hang onto the house after you move out in 4 years. That's a terrible idea. Investment properties should be at a maximum value of 10x the yearly rent. I wouldn't pay more then 72K for a house / apartment that rents for only 600 / month (and even then I would look for a better deal, which you can find if you time things right).
Don't believe me? Just do the numbers. Renting your 200K house for 600 / month is 7200 / year. Figure you'll need to spend 1% / year (I'm being optimistic here) on maintanence / vacancy (and I'm not even considering your time dealing with tenants). Plus another 1% or so on property tax. That's 4K / year, so your total profit is 3200 which is a return of only 1.6% on your 200K. You can get 1% in an ally savings account for comparison.
Really you are much better off investing in a diversified portfolio. You only need 6 months living expenses in cash, so unless your family is ridicuouly wealthy (In which case you should be asking your financial planner what to do and not stack exchange), I have no idea why your parents have 200K sitting around in a savings account earning 0. Open a vanguard account for them and put that money in VTI and your family will be much better off 5 years from now then if you buy that money pit (err house). If risk is a concern, diversify more. I have some money invested with a robo advisor. They do charge a small fee, but it's set it and forget it with auto diversification and tax loss harvesting. Bottom line is, get that money invested in something, having it sitting in a bank account earning 0 is probably the second worst thing you could do with next to buying this house.