its only unsafe if you have something bolted to it in that area... ie a seat ripping out of a soft floor would be unsafe. otehr than that i guess you could stick your foot through it.
the floor adds SOME but not much rigidity to the hull. its usually glassed in with only a few layers of mat, not multiple layers of roving and biaxial cloth, etc for strength. some boats dont even have floors.
as far as the cost, its just plywood, fiberglass, and resin. and a bunch of hours of cutting it out and replacing it. you can do it yourself or i think some dude here recently had his redone for like $1000 in a 18 footer. i have a ton of pictures of my floor being redone in my build thread if you have any questions.
as far as carpet i bought mine from
www.boatcarpet.com for a couple hundred bucks. i got the 20oz carpet and its nice and thick and comfy on the feet. you apply it using outdoor carpet adhesive found at home depot for like $12 for a whole bucket. trim with a blade and good to go for years.