EPS is probably looked more at by analysts who follow the projected EPS number by the company and develop their own whisper number where Wall Street predicts EPS depending if company sandbags or under estimates or over estimates their forecasts. You can see huge drops or increases in share prices when companies EPS beats or under performs the EPS forecast.
Companies also use the EPS number for dividends mostly a percentage to derive the payout.
The value of a stock, or any asset, is the (net present) value of the future cash flows, which generally means earnings. Investors want to know an estimate of the future earnings and how fast they are growing.