While I don't know the answer for sure, as I don't know every construction brand out there, I see enough problems with the brick size you mention that I doubt anyone would manufacture it.
Children older than 5 all the way to adults prefer regular LEGO elements because they are big enough to create impressive models, yet small enough to add intricate details. They are also just the right size that most children and adults can easily manipulate with their fingers (compared to, for example, NanoBlok pieces that many adults find frustratingly small).
The larger LEGO DUPLO bricks are specifically sized for young children 1 1/2 to 5 years old. They are carefully sized to make sure young children won't be able to choke on them. The larger pieces also allow young children with less coordination to work with, and gradually improve their skills. Also, DUPLO and LEGO bricks are compatible in more than just they way they can stack on each other. For example, the holes inside DUPLO studs can accommodate certain regular LEGO pieces.
There is a lot of science and research that go into making LEGO elements; they must be age-appropriate in both theme and difficulty, they must be safe for a particular age-range, and they much fit into the LEGO system by being compatible with other pieces. The brick size you are talking about would be too small for young children (and thus not safe), and too big for older kids and adults. If there is no target market, why would anyone make such bricks?
The only scenario I could think of is perhaps an old brand from the 1950s-1970s, when LEGO type construction toys were just starting out and manufacturers were experimenting with different sizes and ratios. Once the leader emerged (LEGO), it made more sense for similar brands to align their products with LEGO, or differentiate themselves with a completely unique system (i.e. K'NEX, Lincoln Logs, etc.). What you are asking for is somewhere in between (still LEGO compatible but not quite), which would make little sense businesswise.