The main purpose of leaving the HQ undefended is to low in victory points. Background: Victory Points for the most part determine the level of opponents on your map; the higher your victory point score the more difficult your opponents are. The game is set up in such a way that increasing in victory points is easier than decreasing, as there are only three ways to lose them. These include losing Freed Villages due to Blackguard invasion, losing Resource Bases, and having your home base destroyed.
Since there is a cap on how many invaded islands that you can have on your map and Resource Bases are limited in terms of hostile takeover, the only sure fire way of dropping in Victory Points is having your base destroyed. This is why an HQ may be undefended for the owner of the account has reached a point in which his opponents are too much for him to handle anymore and other players who are matched with him are overpowering his base.
Losing VP will eventually get you into the right difficulty range so you can defeat bases and continue with upgrades.
This is true not only for opponents who appear on your map but also for those who attack your base. VP count is not the primary consideration used to determine player matchups, it is the only consideration! It is a flaw in the design of the game which leads players to artificially reduce their VP count in order to compete against those who pay $$ for upgrades and, therefore, have a lower VP count for their XP level.
I never had a need to put my HQ on the beach. While I was rusing my way to HQ 20 I barely upgraded defenses. So my base was mostly taken down with minimum losses. Only when I had two strong prototypes I received a few diamonds over the week. When I reached HQ 20, maxed out (for HQ 20) LCs, primary attack, etc... and started destroying everything on the spot, then my opponents (and attackers) gradually became maxed out bases who often came at full boost. I have no ice and so they do not care even if I put any two prrototypes.
I have not paid a dime to play this game and with a very few exceptions I was able to take down most of the bases, which I encountered so far.
Unless you are at (or near) radar 20 and above around 600 VPs, then you VP will stop (or almost stop) dropping once you reach your invasion cap (your radar will say that you need to destroy some bases before you can get a new invasion). I monitor a few low level twink accounts, which are not very active. Once in a while they go into rampage and clear the map. Then over a few days they will have a few attacks on their bases and then nothing or almost nothing.