Reading all of the posts since my previous I've changed my mind:
1) You stated your mother thinks the carpets should be ripped out, due to heavy staining and the thought of someone else's dirt that may not completely be removed. This is probably the top reason. If your mother is happy, EVERYONE ELSE IS HAPPY!! If mom's not happy with results of cleaning and she's short $700, no one else will be happy either.
2) 2000 sq. Ft is a lot but not too bad. I am a Realtor. Most consumers moving to another house usually end of putting about 2k into a house in-order to bring paint and floor surfaces up to their standards whether its for color matching, worn condition, cleaner feel or all of the above.
3) This carpet is revolting and is probably older than you think. Pet urine, random stains, accumulated dirt. Carpet cleaning does some stain and appearance improvement but carpets don't disinfect well.
4) You stated the carpet is NOT glued down. Labor is one of the major factors for carpet removal when it comes to people minds. They don't want to move the furniture and older carpet removal etc. adds heavily to labor so higher installation fee.
5) Your moving in, the house is most likely unfurnished. This is the absolute BEST time to get new carpet, put it in now instead of in 2 yrs or directly after having it cleaned when you realize that cleaning it didn't bring it back to what it should be.
6) $700, is that tax included? In addition to aggravation of who's doing it, their job performancte, drying time, and questionable end result.
7) You like the carpet that's in the house!! This makes shopping for new carpet easy. Cut off a section of the carpet that may still be clean. Bring it to the carpet store and tell them-- "We want this" Now you're taking the same $700+ from the carpet cleaning but investing it into a smarter media. Clean, fresh carpet and now thanks to this forum, you know the best vacuum cleaner for maintaining it properly in addition to the best upkeep for 6 month or annual carpet shampooing.
Just my advice from working with buyers & sellers of real estate, my own personal life experiences, my work experience in house cleaning and my passion and knowledge of vacuum cleaners and a clean house. My dad is a doctor, my uncle is a doctor and my deceased grandfather was a doctor. Financially, health reasons, smart investing, cleanliness and convenience of move in, my family would recommend replacing the carpet now.
Best of luck and congratulations to the decision makers of the household and new homeowners in which ever direction they decide to go with on this subject. Good luck with the move. I truly believe you will enjoy the new house better with fresh allergen, and germ free carpet.
Blessings to all and happy vacuuming from Central Pennsylvania,
Rob