Yes, market cap should be independent of number of shares, and the market cap = # of shares * $ per share formula still holds, which is why many prefer to think about market caps rather than accounting units.
But it's also the case that a firm issuing a share for the price of $15, increases book value of the firm by $15, and this directly offsets the resulting shareholder dilution. Arguing it was impossible to find buyers at 24 dollars a share is a bit silly, given that the market immediately did just that.