In the United States, checks are a consumer payment system subject to US law. The bank is one of the middlemen in the payment. All such payments are, again by law, reversible if everyone authorized to initiate the payment from the sending account denies that they authorized the payment.
When you receive a consumer payment, it is your obligation to return the payment if the payment was unauthorized. You should not accept a consumer payment unless you know that the payment was made by someone authorized to make it and you are legally entitled to receive the funds. You should know that if the payment is denied, the middlemen will disintermediate themselves from the payment.
That means you will need to sue the person who owed you the money.
Now, taking your questions:
Isn't a bank in better conditions to verify whether a check is legal or not?
How would that work? You would have to explain to the bank the legal basis for why you were entitled to the payment and they would investigate if it was correct? Would you have to provide a statement that you provided services?
You, presumably, know who sent you the check. You must have some way to contact them. Your bank has no such contact.
Wouldn't making the bank responsible help alleviate this scam scourge?
No. I'm not sure what the scenario you're envisioning is, but I can't think of any that eliminates the scams. Are you suggesting the bank just pay out on any such scam? Then it would become a way to scam the banks.
Are you suggesting that banks would have to investigate the legal entitlement of the recipient for every check they accept? How would electronic checking work in that case?
Are you suggesting that payments not be reversible when the sender denies they authorized the payment? Then it would become a way to launder money stolen from hacked computers with the liability being placed on the person whose computer was hacked and no incentive for the beneficiaries of the scam to stop scamming. (The "victim" would be rewarded in this case because they get to keep part of the stolen money!)