To put it in very (VERY) basic terms, assume Company A and...

To put it in very (VERY) basic terms, assume Company A and Company B each have a share price of $1 and each have 1,000 shares on issue - both have a market cap of $1,000 ($1 x 1,000), and assume they merge.

The new Company AB now has 2,000 shares on issue, a combined market cap of $2,000 which means a share price of $1 (i.e. the same as pre-merger). This assumes no other market forces and everything else stays the same.

In your assumption, it would mean that the share price of the merged company is $2 (adding $1 and $1), which means that because there are now 2,000 shares on issue, the market cap of the merged company would be $4,000 ($2 x 2,000 SOI). In simple terms that's incorrect to say that a merged company would have double the market cap assuming everything else stays the same.