It is a bad idea in my opinion to sell BTC and LTC to buy Doge, because almost every movement of the altcoin price increase is caused by BTC, and the new Doge price movement is supported by a businessman is Elon Musk, and means the rise and fall of Doge prices depend on him.
I agree with your opinion but exchanging among coins will earn you the profit here. Ignore the fees.
As per the chart in coingecko, BTC has gained about 550% while DOGE is at 24000% in 1 year.
I'm not an expert trader. My thinking may be wrong but what I find as per the above values, the margin is high for DOGE.