I’m not sure why you’re trying to minimize the severity of the situation. I will reiterate that it’s an extremely bad idea to do this.
Just because you know people who do this, does not mean that it is fine. I will also clarify that this is not illegal, this is not something over which your immigration status in Canada or the US will be impacted.
The entity that gets screwed over is your employer when this gets scrutinized (assuming you did this without their knowledge). The only time an employer will be a willing participant in this scheme is if they have no presence in Canada whatsoever nor do they ever plan to operate there. In that case CRA is toothless and Canadian law doesn’t really apply to the employer. But no other employer will allow for this.
Let me share a hypothetical scenario, you are employed by a US employer who you tell that you work from lets say Washington State (Keeping this simple as WA doesn’t have state income tax). In reality you work from BC. Your arrangement works great as you work remotely most of the time and go to the office a few times in the year when needed. In terms of filing your taxes each year you pay income tax in Canada and the US, get a foreign tax credit towards the Canadian federal tax and pay the entire BC income tax. A few years down the road, things turn sour and the employer decides to let you go (not that this would ever happen, but this is a hypothetical scenario so lets play along). You now go and file for unemployment benefits with BC and CRA who deny your application because there were no EI contributions made by you. Enraged you appeal this and explain that you were employed this whole time, paid your taxes and EI premiums. Now this goes to a review and they find that you were indeed employed. It is the Employers responsibility to remit CPP and withhold the EI premiums. They are found to have been in the wrong and asked to pay these with interest and a fine is levied against them for not being in compliance with the law to boot. If they have a subsidiary or presence in Canada they have no option but to comply if they have no presence whatsoever in Canada then they are outside the ambit of Canadian law.
Now put yourself in an employers shoes and ask if you’d want to be put in this position. Most employers will not want to end up here and this is the reason why businesses like PEOs exist, alternatively business will not directly employ people but will bring them on as Contractors.
You said you weren’t aware of CPP, information about contributions can be found here. Note that this is not voluntary or optional, the first statement makes it clear that this is mandatory.
Next you say -
If you don’t pay EI, you are not covered by unemployment insurance, that’s it.
I’m guessing this is your personal opinion, because this is certainly not factual correct. Paying into EI is not optional. More information is available here. Given the choice every Tom, Dick and Harry would rather take a higher take home vs contribute to EI and CPP, this is why the responsibilities of collecting these have been assigned at source to employers.
For many years I worked in the US on a L1 visa, during all those years I needed to contribute to EI even though I was ineligible to ever receive a payout from EI, because one of the conditions of getting paid from EI on job loss is that one has to be willing and able and to actively be looking for a Job. Whereas one of the stipulations of the L1 visas is that you’re only allowed to work for a particular employer and upon termination must depart the US. Similarly employees on H1-B only have a very limited time to find alternative employment, they too must however contribute to EI.
Lastly I want to reiterate, that I’m not providing advice nor judgement on your or anyone else’s working situation. Each individual is free to pursue an arrangement that works for them, but when they choose to do so it is extremely important to understand the tax implications towards yourself and to some extent towards your employer. It’s also important to keep your employer appraised whenever you move (even domestically) because taxation is a weird beast and also because your employer needs to send you important communication in regards to wage statements and medical insurance amongst other things.