You could do this as an air purifier, but it will primarily just remove particulates and other HEPA-y things. It won't actually bring fresh outside air in.
You could glue a fan to an air filter and then position the thing in a window, to bring in outside air that then gets scrubbed by the filter. But now you're bringing in cold air in the winter, or hot air in the summer.
An ERV brings in fresh air and mostly solves the problem of having cold air rushing in on a winter day, or hot air rushing in on a summer day.
Or open windows, but outside's cold in many places this time of the year. Energy recovery ventilators run stale outgoing air through a heatsink to pre-heat incoming fresh air to save heating costs. Sounds BS but it's a well established and widely used thing.
Air filters remove particulates down to some size, varying based on the filter. They do not scrub CO2 or CO, nor do they (generally) remove other things like VOCs - unless they’re really, really expensive filters. Opening a window exchanges all that junk to be roughly equal to the baseline of your environment, which for most people is at least lower CO2 levels.
You could glue a fan to an air filter and then position the thing in a window, to bring in outside air that then gets scrubbed by the filter. But now you're bringing in cold air in the winter, or hot air in the summer.
An ERV brings in fresh air and mostly solves the problem of having cold air rushing in on a winter day, or hot air rushing in on a summer day.