Any advantages to express Daily ATR(14) as a percentage to its respective daily closing price?

Other measures of volatility like Bollinger Bands (and indicators %B and Band Width) and Standard Deviation (STDDEV) are calculated using only closing data, whereas ATR incorporates highs and lows. So there is an argument for an indicator like the one you suggest.

On the other hand, closes can't move much unless the highs and lows do also, so the existing indicators mentioned are probably serviceable. If you wanted to capture stocks with longer term volatility you would probably use longer parameters, or maybe MAs of the standard parameters, or higher time frames.

What the existing indicators wouldn't capture so well is a stock that frequently makes wicks or tails, but closes near the previous close instead of either extreme. If you could scan intraday, the existing indicators would probably pick up those stocks. Probably, you would only want to trade those stocks intraday also, if at all, especially if you use stops.