About bike shoes?

Your riding is casual, short,  rides. You don’t need all the aditional gear AND the costs that go with it. Have fun!

Cycling-specific shoes combined with a retention system will help you ride further and faster if you're into performance. But for a trip to the park, performance doesn't matter. Go ahead and use tennies and flat pedals, you'll be fine.

You'll ride faster, farther, and with less effort with decent bike shoes. Even on my racing-style road bikes, I prefer pedals and shoes that use the Shimano SPD system of cleats. The shoes are not quite as stiff-soled as real racing shoes, but the cleats are recessed into the sole, so it's possible to walk around normally when you get off the bike. It makes waiting in line for an ice cream cone much more comfortable. (If only we could wait in lines for ice cream cones!)

If you want to walk around in the park it is kind of hard to with bike shoes.

The soles are stiffer. Allowing greater performance while pedaling. Faster with less energy. You will notice the DIFFERENCE IMMEDIATELY.  $100+ shoes worthwhile if a serious cyclist, $900+ bicycle (only down side is needing to carry/have regular shoes when done with commute)

Me I ride a hybrid, 9000+ miles yearly. And wear sneaker-boots. 511 tactical range master boots.(discontinued, best I've ever used) Also 511's norris sneakers. (both flexible like sneakers, but stiff as boots) (comparable to bicycling shoes)

If choosing sneaker boots. try to get lighter weight. Also types hikers highly recommend, mainly for balance (balance = better stiffer soles which improves cycling capability)

ALSO

specialized makes a wide range of shoes. Shimano has better pedals. 

They help you pedal more efficiently because they clip to the pedal, and they're lighter and more streamlined than sneakers. If you're going on a longer ride they're a great option, but they're by no means a requirement. Plus, your shoelaces could get caught in the pedal/chain.

BUT, if you're spending thousands on a road bike, get the cycling shoes. FWIW mountain bikes and/or hybrid bikes work much better for wearing sneakers.

If you’re only going to pootle around casually, at low speeds and short distances, you can use pretty much any shoes.

Although I strongly suggest you use a pair with closed toes. I’ve seen what accidents while riding barefoot can do, and it isn’t pretty. 

For more dedicated riding there are both efficiency and comfort gains from having shoes with stiff soles. And even foot retention systems.

Riding hard in soft shoes eventually becomes like climbing a ladder. Each stroke/step, your foot deforms over the pedal/rung. It does contribute to discomfort and fatigue.

Two part answer.  Part 1) For a leisurely ride to the park - around a few times & back home, there's not a damn thing wrong with tennis shoes, sneakers or whatever you wanna call 'em - IF they meet one specific requirement.  To see what that requirement is, keep reading.  

Part 2) Cycling specific shoes fulfill TWO purposes.  A) As you already know, they keep your feet locked onto the pedal until you unclip.  B) They have a very stiff sole!  A stiffer sole transfers more of your power to the pedals & throughout the bike's drivetrain.  The problem I've seen with 99% of sneakers on the market is...a very soft & flexible sole.  Once you've compared your 'power output' with sneakers vs, cycling specific shoes & cleats, you'll notice the improvement immediately.  

I was fortunate enough to find a pair of sneakers through (of all places) Kmart 😲 with a VERY stiff sole.  Pic below.  Sadly, I don't see them anymore on the Kmart website.  They also lace up fairly high ensuring a snug fit.  If (BIG IF) you can find a similar pair with stiff soles, your ride will be much more enjoyable & probably faster.  For the casual cyclist or 'weekend warrior' - no, there's not a thing wrong with a pair of stiff soled shoes.  I own 2 road bikes.  One has Shimano SPD pedals.  The other, plain old MTB pedals.  Depends on how far I want to go & at what pace.      

Often times bike shoes are designed to where they can be attached and unattached to pedals.  This design is much easier to use than toe clips would be if you have a lot of stop and go on your route.

Regular shoes and no clip means you only get power from the down stroke.  Clips or cleats allows you to get power in the up stroke as well.