Capsaicin cream primarily alleviates localized pain through its effect on substance P, a neuropeptide involved in transmitting pain signals in the peripheral nervous system. When applied topically, capsaicin activates the transient receptor potential vanilloid 1 (TRPV1) receptors on nociceptive nerve endings. This activation initially causes a burning or tingling sensation but, with repeated application, leads to the depletion of substance P from the nerve terminals.

Substance P is essential for the transmission of pain impulses from the peripheral nerves to the central nervous system. Its depletion results in a reduced ability of these nociceptive neurons to transmit pain signals, thereby producing an analgesic effect. This mechanism is markedly different from drugs that block ion channels or inhibit enzymes involved in inflammation.

To summarize:
- Capsaicin activates TRPV1 receptors on sensory neurons.
- This activation causes release and subsequent depletion of substance P.
- Decreased substance P leads to reduced pain signal transmission.
- The analgesic effect develops over time with repeated applications.

Other options are incorrect because:
- Option 1: Blocking voltage-gated sodium channels is the mechanism of local anesthetics (e.g., lidocaine), not capsaicin.
- Option 3: COX-2 inhibitors (e.g., celecoxib) reduce pain by inhibiting prostaglandin synthesis, unrelated to capsaicin.
- Option 4: NMDA receptor antagonism affects central sensitization, typical of drugs like ketamine, not capsaicin.

Reference: Goodman & Gilman's The Pharmacological Basis of Therapeutics, 13th Edition, Neuropharmacology Section, Chapter 16 / Page 450