There shouldn't be "mass layoffs" for that reason. If they are both reasonably large companies, the size of the HR department depends on the number of employees. When you merge the companies, the number of employees initially stays the same, hence there is no HR to be fired. You might consolidate the HR departments, and this might lead to some roles becoming redundant, but not on a mass scale. Similarly for accounting, marketing, etc.

The fact is that there are no synergies for many companies, even companies operating in the same industry. The reason for promoting a merger between such companies is exactly that they will see reduced competition and hence greater profitability. The ideal merger is actually between companies making different products, where the one company can benefit from more vertical integration.