Why don't warts caused by HPV spread to the whole body?
Plantar warts grow deep into the skin and slowly [1]. It is a common thing for warts to multiply [1], but because of the slow growth speed, their symptoms [2] and the self clear-up [1] they can't end up by covering the entire skin surface of a previously healthy person.

There are cases of generalized warts in patients with immune deficiency like hypogammaglobulinaemia, impairment of cell mediated immunity [3]. The immune system plays an important role in limiting warts. There is also a case of generalized facial warts in a patient with no other known medical condition [4].

References:


American College of Foot and Ankle Surgeons, Plantar Wart (Verruca Plantaris)
MAYO Clinic, Diseases and Conditions - Plantar warts.
Reid TM, Fraser NG, Kernohan IR. Generalized warts and immune deficiency. Br. J. Dermatol. 1976 Nov;95(5):559-64. PubMed PMID: 1086679. 
Semon H. Papillomatosis: Generalized Facial Warts. Proc. R. Soc. Med. 1935 Dec;29(2):90. PubMed PMID: 19990539.