D+D->He is impossible because it won't conserve energy and momentum.
D-D reactions emit a neutron or a proton.
At present-day technology, and in any future even very vaguely foreseeable, these reactions are very easy to produce (a fusor does it on a table) and completely impossible to use for a net energy production.
A very simple reason is that D-T fusion is still very hard to harness for net energy gain, yet D-D needs horribly more difficult conditions (see Lawson criteria).
Sadly enough, D-T is the only reaction "at grasp", but would be very polluting because it needs tritium. Tritium isn't available from Nature; uranium reactors produce it presently but will always produce more electricity when making tritium than D-T fusion consuming it, so fusion reactors have to regenerate their tritium to be meaningful.
Now, one D-T fusion produces one neutron, but one neutron is needed to regenerate a tritium from lithium, so you need a neutron multiplier to overcome the losses. As it looks, only lead as a multiplier has a chance to achieve regeneration, and lead spallation to obtain the neutrons is about as dirty as uranium fission producing the same energy.
Any fusion reactor using D-T has that fundamental problem: tokamaks, stellarators, and laser inertial fusion as well. Z-striction machines could cope better if some day they can fuse other nuclides, like D-D or p-B.
This pollution issue was known from specialists but not widely enough until I argued about it at Saposjoint.net and Physicsforums.com; now Wikipedia includes this rationale. To my eyes, it makes fusion reactors uninteresting unless someone finds a convincing solution, which hasn't happened in the last two decades.