Earlier quoted context omitted.
I'd always recommend anyone using the free tier to add a free billing alert to your AWS account. For example when I had a free tier server, it cost me roughly $5/month, so I had an alert set to $15/month. When my free tier ran out (I got the month wrong) the alert notified me ($16 in charges) and I purchased a reserved instance to bring the cost back down to under $10/month.
Until / unless there is a way to actually put a cap on billing (not just a notification), it's something I'll stay away from when I can.
Although I do think a soft cap (preventing more Ec2 launches etc) would make a lot of sense.