Can I use flat pedals?

As mentioned there have been some studies done (one very recently) that suggest no difference in power transfer between being clipped in or not.

The discussion should really be centered on intended distance and support for the feet.  Over a short distance there's probably not much of an issue but over a longer distance you would want the stiffness and support that a cycling shoe would offer over something like a running shoe.  Take your running shoe and bend it.  It bends and flexes quite easily.  Now try that with a cycling shoe.  They don't bend.  There's a reason for that.

If it's bad to use platform pedals instead of clipless pedals/shoes, then 50 million kids are just doing it all wrong...

The biggest concern with regular shoes and platform pedals is to make sure your shoe laces aren't dangling where they can get wrapped around the pedal spindle.  When that happens, you won't be able to pedal and you won't be able to get your foot off the pedal and it's usually a surprise so you'll likely find yourself on the ground.  

If you aren't comfortable with clipless pedals/shoes, ride the platforms.  You'll give up a little efficiency.  

I've seen far more catastrophes from people using clipless pedals than platforms.  In triathlons, the mount/dismount line is the most likely place for someone to fall over trying to clip in/out.  

KEEP those shoe laces tucked in!

If using something that makes you uncomfortable and tense and might even keep you off the bike, then it's not "bad" to get rid of it.

However, there is a reason that any pro cyclist or triathlete, or even cycling enthusiast use clip less.  Yes, the learning curve can be scary (and even painful) but after 20 years of using them, I can't even fathom going without.  ESPECIALLY when mountain biking when the rough terrain can actually have your feet slipping off platforms.

I would suggest do what's comfortable if you must, but I would really work on getting over the clip-less fear.

What kind of clipless pedals do you have? Some types (like SPD) are harder to use than others (Speedplay, say) and some people find it hard to ever get comfortable using them.

Flat pedals give up so much over clipless.  I have flat pedals on my tandem, and at every moderate or more bump my feet flop around.  I have to pedal carefully to keep my feet properly positioned. I couldn't imagine doing standing climbs with flat pedals.

I completely understand that sick feeling of being locked to a bike while it is tipping over.  It really make you want to ditch the clipless pedals.  But, the clipless are really more efficient and safer for some kinds of riding situations.

I rode flat pedals or pedals with cages for about 40 years before clipless pedals were invented.  I got into some really bad pedaling habits.  I tend to put some weight on the back pedal that works against my downstroke.  The weight is needed to keep the foot in contact with the pedal for flats.  On clipless pedals you can totally take the weight off and hence gain efficiency.  If you have access to a trainer, try this exercise.  Pedal along as normal at first, then try lightening up your feet especially on the upstroke and keep pedaling the same cadence.  It feels so much easier.  This is why it is worth it to learn to use clips for efficiency. And it is better not to get the bad habits ever started.  My poor pedaling technique is a big reason why I am still a back of the back of the pack cyclist.

There is another safety reason for using clipless pedals.  You many never had hit a bump hard enough or fast enough to knock your feet off the flat pedals.  Believe me it is quite possible if you don't see a speed bump in a parking lot in near dark.  The outcome is really not pretty.  Clipless pedals (or straps) keep your feet on the pedals and at least give you a chance to save the crash and the skin.  

I don't know how you went about learning to use clipless pedals but I practiced stopping and unclipping a lot before heading out for a ride.  i went around the block in the neighbor, unclipping and putting a foot down at each corner, first one foot then the other.  I practiced going fast then braking hard to a stop and unclipping too.   I practiced turning the wheel just a bit toward the unclipped foot to ensure that I come to rest on the unclipped side.  Sticking the unclipped leg out a bit helps too if things start going the wrong way.

If you have done the practicing and still don't like them, go with the flats.  I know a few others who tried them and just could not get comfortable.  They will tell you it is not a terrible thing.