This is just to state upfront the type of financing that this specific property can qualify for. Some properties can't qualify for FHA, VA or conventional because of the condition. In your example, they are just making the consumers aware that it can pass these types of financing--for their information.
Cash can buy almost everything.
For your own personal residence there are no limitations and is a good way to buy a property you love that would not appraise out if you had to finance it.
Sale terms are posted to notify a prospective buyer of the terms available for a particular property. Cash always works, conventional financing usually works but sometimes FHA loans will not work if a home will not pass an FHA inspection/appraisal due to condition. Or if located within a condominium association, the complex must be FHA approved. Some properties are in total disrepair and will not qualify for any financing.
Sale terms also reflect the sellers willingness to entertain a variety of offers.
Getting back to your question; Cash is always welcome as long as there is enough of it (:
So, go for it! They should welcome your cash (as long as it's a reasonable offer :) )
Keller Williams Realty Partners