The biggest problem with requiring a credit card with a free trial is that unscrupulous people also use the same tactic. Rightly or wrongly, the pattern "requires credit card for trial == scam" is etched into some people's minds. In order to overcome this, the company would have to be well known and well respected, at least within their niche.
I see how some people's knee jerk reaction upon seeing that a credit card is required for a free trial would be to just close the tab and find a competitor, though.