The Sheplyst isn't Shepard though, it's Faux-Shepard. It may do what Shepard would have done, or it may not.
Too much of a gamble.
Re the relays;
- The current cycles can't build relays, but I don't think anything was said about repairing them, which presumably would be easier to do.
- Even the above might be erroneous, as the Asari had previously floated the idea of building their own relays
- The current cycle's top scientists are all in one place, having just finished building the Crucible. If this cycle is ever going to learn how to make the relays work then surely there's no better time
- The mass relays are Reaper tech - if only we had loads of inert Reaper tech around that could be reverse-engineered to see how it might work...... 
That, honestly sounds like a very reasonable alternative!
My main "problem" with choosing Destroy will always be in the ending slides and their utopian depiction of a world without Shepard. In many ways it feels like the game is rewarding killing off Shepard.
- Destroy, Shepard might live(perhaps) Universe is in dissarray, no way to rebuild, a fake hope from a shitty admiral. Geth and EDI gone forever.
- Control, Shepard dies, but lives as a new catalyst of Sheps memories, hopes and dreams... Nothing lasts forever Geth and EDI, no idea.
-Synthesis, Shepard dies completely...a perferct utopia of peace, understanding, hope and celebration. Where previously genocidal machines decide to rebuild the universe that was and reward the new speices with knowledge of generations past.....
Doesn't seem like a very fair trade to me