Thanks to those who pointed out that Parula is the new default Matlab colormap and solves this problem nicely. I will give a more general explanation of why this problem arises. A very good series of articles about colormaps can be found here.
I'll consider the colormap as a series of colours in Lab space, for reasons which will become clear shortly. In Lab space L represents the colour's lightness and a and b give the colour. Therefore we can view converting to greyscale as taking only the L component (with a=b=0). Therefore to convert well into greyscale our colormap should be monotonic in L and ideally approximately linear.
The 3D color inspector plugin for imageJ provides a handy tool to visualise the colormaps in Lab space. Looking at the Jet colormap (the old Matlab default) in this way the problem becomes clear. Jet is not monotonic in lightness and approaches maximum lightness somewhere in the green/yellow range. Therefore, when converted to greyscale the two ends of the map appear dark while the centre is light coloured.
Compare this to the parula colormap, which is monotonic in lightness. If you do further analysis you can also show that it is reasonably linear in lightness. The conversion to greyscale will therefore be pretty good.
There are many other colormaps which also have this property of monotonic lightness, in particular most monotone maps. However, it is also advantageous to maximise the distance between colours in Lab space to increase clarity when viewing in colour. Monochrome maps are relatively weak in this respect as they have a much more limited range of ab values than rainbow type maps.