I am a drummer - who also plays several other instruments and writes. With that qualification, I think a low cost drum machine makes more sense for a songwriter.
A songwriter should focus on the value of the lyrics, the melody , etc. While some type of drum beat can help establish the rhythem, you don't need to buy, mic & play drums to achieve that. A songwriter (or a good song) does not need complex drum parts - although that may be a factor of a good arrangement (vs. a good song).
That being said - I completely agree that the more instruments one can play (or at least understand), the better musician you may become (and perhaps a better writer).
Although candidly, I find the more instruments I learn I am less of a song writer and more of an arranger. Instead of simply crafting a well written song - I'm already thinking about guitar riff's and drum breaks, etc - sometimes my songs become slaves to all the riffs I'm hearing - rather then being served by those riffs.