swapping out ice bottles is really not that bad. seems like you’re making a bigger deal out of it than necessary.
I don’t think it would be a huge issue… what you are kind of describing is like open fermentation like they do in a lot of English breweries ie. Samuel Smith’s …I would imagine during active fermentation enough co2 would be pushing out that no bugs would get in though the risk is there during the non fermenting times… then you have a Plambic 
You could always use something like this Vented Silicon Stopper. I use these on my fermentation buckets because they won’t fit into my fermentation chamber with a regular airlock installed.
I use the ice bottle method as well and its really easy. I have 1 gal milk jugs, 1/2 gal milk jugs and 12oz bottles that I keep frozen at all times in the freezer in my garage. Depending on how much temp I need to drop over a specific amount of time determines which size bottles I use. I also tend to use the smaller bottles during the day to hold temps and the larger for overnight since they obviously take longer to thaw. After a few days you get really good at choosing which ones are appropriate.
If you do use this method one thing I would suggest is also using a beach towel or something similar at the bottom of your chamber to soak up the moisture from the thawing bottles. I have never had a problem with mold this way and when you feel the towel is alittle too damp, swap it out with a fresh dry one.
Fermentation generates heat, so I’d think fermenting in an insulated container wouldn’t work out well. The temp would just keep going up.
So you don’t use water, just the ice bottles?
I’ve used, tin foil, saran wrap, sandwich bags.
Never had a problem.
If I am leaving it sit for a while after fermentation is done, or cold crashing , I’ll throw on an airlock.
if you have an insulated container yeah. The water provides thermal mass so temp swings are moderated because it takes so much longer for all that water to change temp. The insulation in your cooler provides insulation instead so that moderates ambient temp swings by isolating your fermenter from them.
i use frozen ice packs. just switch them in and out periodically,
yeah no water, just ice bottles. I made a fermentation chamber out of a rubbermaid tote using reflectix insulation (inside and out) and it holds temp within a few degrees for hours. I usually change out the bottles once in the morning and once at night but I check it a few times during the day as well but hardly ever have to add more bottles unless it is really scorching outside.
Have you tried water bottles too or just the ice packs? I bought a bunch of ice packs from either lowes or walmart, really cheap like .50¢ each, but they don’t stay cold very long at all. I stopped using them because the water bottles lasted atleast 4x longer.
i just use ice packs, the foam gel ones. we get vaccines shipped with these and they would otherwise get thrown out. works very easy for me. i just put them around the bucket in an insulated chamber and voila. depending on the outside temperature, but even in the summer, in my garage, i may change half of them every morning. some will stay longer, i just kind of gauge it. and i can keep temp at 50 degrees.