You could achieve this by setting skip_readonly_check to the context.

In general, about How can I work around this? - first of all it's important to find out where/when exactly the error message is raised. The easiest way to do so is be taking the first view words of an error message and search for it in the core source (there could be line breaks and other things going on, so you may not find the complete string in one line - thus, search for a portion of the message). This would lead you to https://github.com/odoo/odoo/blob/18.0/addons/account/models/account_move.py#L3257

Now that you've figured that this message is raised in the write()-method of account.move when skip_readonly_check is not part of the context and the move's state is (or is becoming) posted and a unmodifiable field is to be changed, you can try to find the least intrusive way on modifying the behavior. 

One options is, as stated on top, to pass the context key skip_readonly_check under certain circumstances, namely, if nothing else but the purchase_price is being set. You could do this for example by evaluating the vals dictionary passed to the write() method:

class AccountMove(models.Model):
    _inherit = 'account.move'
    
    def write(self, vals):
        print(f'vals: {vals}')  # vals: {'invoice_line_ids': [[1, <line id>, {'purchase_price': <value>}]]}
        if set(vals.keys()) == {'invoice_line_ids'}:
            # The only change to the account move is a change in of oe or more invoice lines
            for line_command in vals['invoice_line_ids']:
                print(f'line_command: {line_command}')  # line_command: [1, <line id>, {'purchase_price': <value>}]
                if line_command[0] != 1 or set(line_command[2].keys()) != {'purchase_price'}:
                    # A field other than the Cost is changed on an account move line
                    break
            else:
                # Nothing but Costs are changed on invoice lines, thus it should be safe to
                #  skip the readonly check (relevant to posted moves only)
                self = self.with_context(skip_readonly_check=True)
        return super(AccountMove, self).write(vals) 

It should be mentioned that this is not a final solution since other fields of an account move may need to be editable as well, for example the due date; while it still is editable, using above snipped unaltered will not allow you to change it along with a change in cost at the same time, because vals then would be something like

{'invoice_line_ids': [[1, <line id>, {'purchase_price': <value>}]], 'invoice_date_due': <date>}

and therefore the first if-condition would be False.

Side note: why the cost of a product needs to be tracked on the invoice is a whole different story. Sale Orders would allow this by default already.