Anyone used masonry paint without using anti-fungal wash first?

[unlucky83]

I want to paint my outside window sills.
Concrete, were covered in green slime and moss. I jet washed some of them and removed the worst of the green and the moss but can see the moss has start degrading the concrete. They still have a few black spots on (lichen?). So I decided best to paint them.
After spending ages in B&Q, I bought black masonry paint, Dulux Weatherseal not B&Q own label because it said it contained a fungicide and was splash dry in 5 mins.

Now read the instructions (I know ...) and it says I need to give the surfaces an anti-fungal wash first. That stuff isn't cheap and would involve another 10 mile return trip and time etc.
I can paint them easily (from inside upstairs -so no faffing with a ladder etc) - just wondering if the wash is really important? Can I just touch them up if nec? Or will it be a complete disaster?

Read somewhere about washing with weak bleach instead - but IME bleach doesn't even kill grass...(and will need to let it dry and then rinse off etc)
I have vinegar (actually more concentrated acetic acid) that I know does work as a 'weed killer' - but it will stink and like the bleach I'll have to let it dry and then rinse etc...
If I was doing walls, up ladders/scaffolding etc I would do the preparation properly - but for this? Is it really necessary?

If a surface has moss, or dirt, or mould, or fungus, or lichen on it that you do not clean off, then you are painting the moss etc.

When the moss dies the paint will not be attached to the bricks so will bubble or flake or fall off.

You have to prepare the surface before painting.

Thanks - I do intend to clean it first - remove the moss, dirt, worst of the algae - the lichen is more of a problem. Have jet washed the downstairs ones - upstairs will be more problematic.

I read something about needing to kill off the fungal spores -but surely they couldn't grow if the paint has a fungicide anyway?
I could just paint on weak bleach first I guess. Do you think bleach will work?

And if the paint flakes - can I just scrape the loose off and touch up - or will that look dreadful? (And be a real pain)

(I'm a little cynical about primers etc - years ago I gloss painted my light switch and light pendant (red - I was an 80s teen) - my dad said it would chip off...about 20 yrs later (when he realised I really wasn't going back to live!) he had to change them to get rid of it - the light switch just had a few tiny chips....)

Bleach will do. Once dead and dried out, a stiff brush will clean away the moss remains.