1) They accumulate the virus on their surfaces, so that handling them will increase contact, not decrease it.
So they can indeed block out the virus ... yep.
Better to write: they might accumulate virus on their surface, so that handling them could increase contact (... and handling a mask should be followed by hand washing).
2) People wearing the masks tend to touch their faces to adjust the things more often, not less, than they would otherwise touch their faces, increasing risk.
This is in the realm of anecdotal. If you wear a mask regularly and get comfortable with it, then this problem is greatly diminished. And it's not really just touching your face, but more not touching your mouth, nose, eyes. Personally, I definitely find I touch my face less having a mask reminding me not to than if I didn't have the mask on.
3) False sense of security.
I find it the opposite. The mask puts me on alert and reminds me to take other precautions, to not touch my nose and to do so with tissues when necessary (I have a fair degree of allergies). Seeing everybody you meet wearing a mask does not provide a sense of security. It more induces a sense of concern and alertness. It encourages more precautions.
COVID-19 (or SARS-CoV2) is more contagious than the flus have been. It's easier to catch if you are exposed and they find facemasks don't reduce exposure.
The coronavirus is transmitted through water droplets emitted from an infected persons mouth. Either through the air in water aerosol droplets or on surfaces where such droplets land. The infected person might be asymptomatic, presymptomatic or experiencing symptoms. At any of these stages they may be contagious, as far as is known.
Which means you or anyone you run across may have the virus and be able to transmit it. If everyone is wearing a mask, some are keeping most of their viral load to themselves via a mask, and others are less exposed and keeping out much of the viral load those not wearing masks are emitting.
How this isn't helpful is hard to fathom.
Simply, if you have some degree of covering protecting your mouth and nose from the external world, you are safer and better protected than if you don't. I don't see how this is even debatable.
Nobody is arguing that wearing a mask is 100% protection. Or that mask wearing shouldn't be combined with other precautions -- social distancing, limited public exposure, hand washing, non-face touching.
I see qualifications that you don't need to wear a mask in a low-risk environment, but that definition is merely based on the numbers of cases reported in any given area, and a low risk environment can ratchet up to high-risk once an outbreak is detected, which means that you should have been protecting yourself, but you were unaware of the true risk level.
Most epidemiologists qualify that if you were in Wuhan you probably should wear a mask. Of course, no one expected northern Italy, or New Rochelle or Kirkland Washington or the Geron conference in Boston to become mini-Wuhans. Precautions are good. Blocking out germs during an epidemic is sensible. Wearing a mask will provide a fair degree of protection, and in conjunction with other measures will prevent infections and save lives.
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