If you are a policyholder with a claim dispute with your insurance company and you have given up the fight and are ready to lose, go ahead and invoke your right to the appraisal process that your insurance company has written into their policy. It will be over quickly and if you are paid anything as a result of it, at best it will be a figure reached through compromise from what someone other than you “estimates” your loss to be with no commitment to perform any of necessary the work for the amount the appraisers and umpire “estimate” it to cost.
There is a reason why your insurance provider wrote this clause and chose to insert it into his contract with you. Judging by his unwillingness to pay you up to this point, that reason is probably NOT because it is likely to result in a significantly higher payment to you.
If, on the other hand, you are growing weary of fighting with your insurance company over a legitimate claim and you want to be fully indemnified but don’t know how to proceed to make that happen, seek the advice of either your attorney or a public adjuster licensed to practice in your state.