You cannot, part of the reasoning will be that the footage may need to be used in court therefore the integrity of the information needs to be maintained, another reason will be that it would be incredibly impractical and a burden for businesses to erase the faces of everyone that requests it. You cannot request that a business deletes CCTV footage of you either, probably for similar reasons. You can request a copy or to view that footage though.

In another comment you posted:

>I'm still not sure that recording everyone who walks past your store 24/7 is legitimate interest.

Stores and businesses need to display signs for when they are recording in the areas they're recording, inside a store it may be obvious that the store is recording, so a sign may only be needed on a door. Outside of a store you may need more prominent signs. If it's not obvious that the area area is being recorded then even more signs need to be posted still. The degree to which stores and businesses can record outside of their businesses will vary by country, but for the UK the ICO provides information for consumers [0], and businesses [1].

[0] https://ico.org.uk/your-data-matters/cctv/

[1] https://ico.org.uk/for-organisations/police-justice/

Security camera footage is overwritten and recycled on a regular basis.

As a matter of fact: If you operate secutrity cameras in a public -, or semi public place you need a written procedure why something is captured, what is captured, how long it's kept, who can see the footage and under which conditions the footage is retained.

"If not, why?"

Because this is not a reasonable request if the footage is anyway deleted after, say, 72 hours.

Read about legitimate interest, it's only a few sentences

The document is 88 pages long. There are 31 mentions of 'legitimate interests'. I'm still not sure that recording everyone who walks past your store 24/7 is legitimate interest.