Why would the bit density have to be the same?
Imagine that the platter is a piece of paper and the write head is a pen. The head can write, say, 1000 bits per second by being raised and lowered to make marks on the paper. Writing one bit corresponds to lowering the pen for 1ms. If the sector is close to the centre, the paper will be moving fairly slowly, so holding the pen down for 1ms will leave a short line; if it's towards the edge of the disc, the paper will be moving much faster and 1ms will leave a longer line. Now consider the read head: wherever it is on the disc, if it sees ink for a millisecond, that's a 1; if it sees paper for a millisecond, that's a 0. The data density is lower at the edge of the disc but the heads can do their job without needing to know where on the disc they are. What you might call the "temporal bit density" (a term I just made up) is constant across the disc.
In contrast, if you wanted the "spatial bit density" to be constant across the whole surface of the disc, then the heads have to read and write much faster at the edge of the disc. In this set-up, each 1/0 corresponds to a fixed length, and that length will come past the heads much more quickly if it's at the outer edge of the disc than if it's at the centre. This is a much more complex scenario.