Are there pedals that are both flat and cleated on each side? I use the same bike for commuting, fast lunch-time rides, and not-very-fast weekend touring. I recently switched from flat pedals to clipless (Shimano PD-M520) but am finding them impractical on my commute - too much clipping in and out, for no obvious gain. I figure a good compromise would be pedals that are part-clipless, part-flat, but all the options I have come across so far (such as the Shimano M324) seem to be flat strictly on the one side and SPD strictly on the other, meaning I'll have to flip the pedal over even when wearing ordinary shoes. Is there a pedal that can be used as a flat pedal on both sides, and as an SPD ideally on both sides too but otherwise on just the one?
I think the most approximate thing, at least on Shimano is the Shimano PD-M424, which is a clipless pedal with a resin cage, or the Shimano PD-M545 which is the same but with an alluminum cage.

I have been using these on MTB and commuting since year 2000 and I think they would fit your needs. The are easy to Clip In an out, but the cage provides very good support when used with regular shoes. I have commuted with those kind of pedals using Tennis shoes, flip-flops and even Office Shoes (with rubber soles). I have used hiking shoes to MTB with them and with good performance.

There are other similar like the Shimano PD-M647.

My father used them too with regular running shoes in light XC riding for years until I convinced him that platforms would be cheaper and more comfortable (He would never use clips).

The only care you must take for serious riding is that the shoe must have good sole texture, so it kind of grabs the center of the pedal and has good grip to the cage, because they are less safe than plain platform pedals.

Another Solution for you are these platforms that attach to the clipless mechanism, converting your regular clipless pedals into platforms. http://problemsolversbike.com/products/deckster_clipless_pedal_adapter. You need to buy extra cleats because the platform adapter dos not include it. This kind of solution would be a little cumbersome as you would have to install the platforms for commuting days and remove them for performance riding.

I'm pretty sure that a skilled machinist with the right tools can craft a DIY version of these, that has a cleat-like shape incorporated so it has a flatter profile. (I have this project in my bucket list)

Finally a tip: your complaint about too much clipping/unclipping makes me think that it is (still) kind of difficult for you to do so, but it shouldn't. As you get more practice, clipping in and out becomes so natural that you won't be counting how many times you do it. Second, adjusting the mechanism tension to a lower setting makes it easier to pull out of it. Personally, I use mine in the lowest possible setting but I don't have unexpected  release issues, and I constantly lift the bike by pulling both pedals up.