The biggest downside to delaying closing is that your lender (assuming you're financing) likely won't lock in your rate for that long and, if it will, it might charge you a higher fee to do so. That isn't necessarily a bad thing if rates are dropping, but if they're creeping up--as I think they are now--then it could be a problem.
Beyond that, if you have the home inspected in April and then something happens to the home in May--say some flooding from spring rains--then you might not be the wiser. If you do delay the closing, then I would ask for the right to do a walk through of the house a week or two prior to closing.
Would you incur any extra costs by having to delay closing, e.g., storage fees or the like? If so, then you might consider asking the seller to bear or share those costs.
I'm sure there are other potential issues, but that's what comes to my mind most readily.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
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