Board Game Arena

Is there any allowance or infrastructure in place for developing and competing with computer-controlled players on this site?

As far as I know, no, there isn't. The closest to it is when a player leaves the table, and is in zombie status. However, most games just have the zombie player skip their turn, rather than make an AI type move.

How would people feel about someone writing a bot? Assuming it advertises itself as such.

I have the same question. How does the player community and the developer community think about AIs/bots?
On other platforms the feelings are quite diverse, both pro and opposed.

One end of the spectrum is a very good AI, like available for reversi. As it easily outplays any human, it somehow takes the fun out of playing the game. On the other end is a basic AI which would allow a human beginner to learn the basic game mechanic without destroying his ranking or annoying or slowing down other players.

Most AIs would be in the middle of those extremes. For more complex games than reverse, say Caylus, writing an AI of even moderate strength is quite challenge. For the foreseeable future (say 5-10 years) AIs will not reach the strength of good human players. Still, I could see a case as sparring partner and for beginners to learn.

Any opinions?

I completely agree with the point of having bots to learn how to play. The reason why most game comunities avoid bots is because the don't want people just playing against bots, so at the end you have less opponents.

For me it would be ok if we have bots, but I don't find it necesary. You can read or watch some tutorials, watch a current game, play in turn-mode... There are enough ways to learn how to play a game, and you can always ask other players for help.