Styles of Shoe Covers for Colder Weather After getting this pair of shoe covers,

I'm wondering whether this style of closure (zipper behind the foot) is reasonable.
I suspect that after the inevitable bit of walking on grass and asphalt, they'll be too mucky, and require ongoing cleaning.
The trouble, it seems, is that they must be put on after the shoes. These shoe cover only make sense for cleated shoes. One puts on the shoes, then pulls these shoe covers over the shoes, while adjusting the neoprene so that the cleats and the heels poke through the two openings at the bottom of the shoe covers.
Another style, one with velcro closure that wraps around the foot between the heel and the cleats, seems more sensible.
That style can be worn along with regular cycling clothes. The shoes are put on later, and then it's simply a matter of pulling the velcro shut.
Can you comment? I need these covers as a solution to feet getting too cold, and nearly numb, at just 12°C/54°F. I am looking for a solution that will enable riding until freezing (then I'll park during winter).
Related:
1,
2,
3.
So far I'm riding with synthetic base layers and wool (skiing) socks. I feel that switching to wool base layers and thicker wool socks will be all that's necessary to continue riding until freezing (with thin tires).
Update
It is a very small detail, but it may be worthwhile being aware of it, at least for some.
Style 1, (the one pictured: wear shoes; pull over; zip) requires having some bench next to one's bike. Putting them on without a bench or a seat is significantly more awkward than trying to wear socks without sitting down.
I have 2 sets of shoe covers, and each has its advantages.
One are very much like the ones you show.  These are much warmer and easier to walk around in, but take a little more work to pull on (they are tight to the shoes) and while water repellent they are not waterproof.  They are perfect for riding in cold, dry conditions (down to, say -5C with good socks).  I've never had a problem with the zippers.
The other pair are waterproof cordura-type nylon.  They are mostly open on the bottom, except where they hook over the toe, velcro up the back instead of having a zipper, and have a velcro flap that passes under the arch of the shoe to hold them in place.  They are not nearly as warm and mostly good in heavy rain.  (Although even then water will come up through the screw holes in the bottom of your shoe.)  These are easy to carry (they fold up smaller), and faster to put on, at the expense of being mildly awkward to walk in.
Durability is an issue with both of them.  Pulling the neoprene ones on and off over the cleat has mostly torn the strap under the foot, and the toe part (mine comes partly down over the toe) is mostly abraded away from stepping down.  I have gaffer tape one one of them to keep the toe from popping up off my shoe.  The cordura ones the velcro is not holding well any longer, and I've occasionally had the strap under the foot come loose.  (Fortunately it hasn't gotten caught in anything yet.)