Someone told me that if I change all my accounts to Transfer on Death, I will avoid the cost of probate fees and the cost of estate planning. Is this true?

That depends on what other assets you own and if there is any estate tax owed. Your beneficiaries could be required to pay taxes with no orderly process to do so. If your Will sets up trusts for minor children or disabled beneficiaries, there may be nothing available to fund the trusts if all accounts are Transfer on Death. This is why planning to comprehensively coordinate all aspects of your estate plan for your loved ones is cost effective and beneficial.