I think we (American English speakers) tend to drop pronouns in informal writing more than in speech. At least, thinking about how I'd say things, I might elide the pronoun almoooost to the point of dropping it, but it still "feels" like it's there, even if it didn't come out very much.

But "was thinking the other day, why don't we..." sounds fine to me in an email. wouldn't say it out loud, though...