I think SEO is very well abused in the U.K. and U.S. And everybody gets too many spam emails for SEO services. This is an example of professional deceiving SEO email which my client forwarded me to check the company out:
"Hi ,
I am looking for a plumbing company that is ok with some media exposure.
Can you take on more customers?
Who is the best person to speak to?"
Actually they were trying to sell 2000 GBP/month SEO&SM packages. So the abusers are still out there and they are still hunting for new clients.
Paying for number of keywords in the first page?
I think this is quite wrong, you can rank for keywords which has no or little traffic. Or low quality leads. But if it is difficult keywords with traffic (you need to check monthly traffic and difficulty for that keywords), then it may be ok to use as a criteria.
Search Console Traffic References
Actually they can be manipulated. For example, if company is ranking for a keyword but there is no traffic, the SEO company can create fake traffic by searching that term and clicking on client's site.
I have a client who was using a local SEO agency. After he moved to us, we found his previous agency was creating fake traffic/clicks to manipulate Google Search Console stats. And they were outsourced the SEO to a company from Ukraine.
Here is my client's response when we asked opinion about finding new clients in the U.K.
"[12:57 PM, 4/5/2020] G.S.: SEO is always a hard one to convince people because every person will say the same thing!
Everybody will check the website make some comments and say this is why it is not performing correctly, We can increase traffic...etc etc etc.
[12:57 PM, 4/5/2020] G.S.: Look how long it took you to convince me. And I even knew in the back of my head the other guys that I was working with was not really an expert.
[12:58 PM, 4/5/2020] G.S.: The only thing you can do is keep pushing people...In a nice way.
Like me for example it took you a good six months to catch me and now we’ve been working together for 7/8 months"
Having Industry References?
We had another client who was a dentist. And he said he worked with a guy which was managing SEO of another dental site which ranks very well on Google. But he said they could not get good results from that guy for their own websites. So we checked the site which ranks well, and our opinion for it; the success was not the SEO guy, rather the website is side business of a university, which has very high domain authority with .edu domain.
Result?
So every SEO company will say they are sending space rocket to Mars. And if they want to deceive you, they can provide fake stats. But that does not mean there are good guys out there. I think you can check/call their references, but this can be manipulated too
So the best option is getting referral from someone you trust. Or alternatively, you can ask many questions to the company related to SEO which you know the correct answers. There are many blog posts about which questions to ask SEO companies before hiring.