MDF is very smooth, very dense and beautifully flat. But it's actually not very hard. It's almost too easy to pierce, cut or otherwise damage with anything hard & sharp. It tears out easily when overtightening screws in it. To some degree, it's even easier to cut, gouge or pierce accidentally than other true woods. In terms of how easily it cuts and tears, it reminds me more of paper or cardboard than wood. MDF is essentially made similarly to paper, being very fine wood fibers bound together in a resin, under pressure.
I use MDF with various compounds, including chromium oxide, aluminum oxide and diamond paste. It works well with any of them, and the compounds don't have any trouble embedding into it. Diamond is orders of magnitude harder than any wood, or even steel - so it can embed in most anything under some pressure.
Other woods like basswood also work well. Most any tight-grained wood that's smooth & flat will do, like basswood, pine, poplar, oak or maple - I've used all of these at one time or another. Basswood happens to be popular mainly because it's not expensive and it can be found in hobby shops already pre-cut to perfect sizes & widths for use as a strop.