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piece of cheap plastic in front of it?

At $55 I wouldn't call it cheap plastic :-?
I had a similar dry-type bag years back. It was no-where that price, but similar in design.
Had the same problems you referenced and I ended just putting in away in the bin of looked good/performed poorly outdoor gear.

I took my point and shoot Samsung this spring/fall and it's not waterproof, so I just kept in a small zip-lock in my shirt pocket.
It never got wet thru heavy rain, but it obviously wouldn't survive a complete submersion.

One think I bought and really liked and will use from now on regardless of camera type is a CHUMS brand neck lanyard made of Paracord.

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It's long enough the camera can be held in different positions but short enough that it doesn't hang down and tangle in things. I kept my camera in my shirt pocket 24/7 which made it easy to get unexpected pics.