Assuming you are legitimately in a position to retire, yes, the house should be paid off.
Assuming you will make enough in the market to cover the payments is risky. Long term probably true but 2-3 down years and it can really eat into your nest egg and the smaller nest egg won't grow back as much the market does bounce back. Mortgage payments come whether the market is up or down. For your typical retiree (ie: you actually are retired, sold the business and don't have a lot of other deductions), the mortgage deduction is a joke. Once you account for the standard deduction, you need a huge mortgage to get anything off your taxes. Even if you do have enough deductions, you are paying the bank $10k to get $3k off your taxes.
Be very careful with financial advisors. Most have at least a marginal affiliation with something they sell (or get a kickback from a related business they recommend). Constantly assume anything they tell you is in their best interest and much of the training they have received has been molded by the investment industry, so even if they are dead on honest, they may not realize that they are giving you poor advice. This isn't to say you shouldn't consult one but don't blindly follow their advice.