Well there's always MtGox, which I don't think has any limits, but you have to give them an absurd amount of identity verification to be able to place orders, which scared me away.

There are multiple services, Coinbase is just one of them. This particular instance of you not being able to place an order through them is not indicative of a wider tendency to not be able to place orders.

Coinbase has a 24-hour rolling limit for how many coins can be sold through them. This is reliably the case every day.

Also, not being able to buy coins doesn't seem to be a "security" issue.