The Scrum Guide doesn't explicitly prohibit one person holding both accountabilities, and small teams sometimes combine them out of practical necessity. It's worth being honest about why this combination creates structural tension.
The structural conflict of interest
The Product Owner is accountable for maximizing value: sometimes pushing for more scope or tighter timelines. The Scrum Master is accountable for the team's effectiveness and wellbeing: sometimes pushing back against exactly that pressure. One person holding both roles has to somehow advocate against themselves in real time, and in practice, one accountability usually wins out consistently while the other becomes nominal.
What gets lost specifically
Genuine team advocacy. A separate Scrum Master can push back on a Product Owner's request in a way a combined role structurally cannot.
Process integrity under pressure. A genuine Scrum Master can hold the line on practices that matter for long-term health even when short-term pressure argues against them. A combined role has a direct incentive to relax exactly these practices when they're most needed.
A trusted, neutral facilitator. Difficult team dynamics are harder to raise with someone who is also, in the same conversation, the Product Owner being potentially discussed.
When it might be defensible anyway
Very small teams sometimes genuinely have no better option than combining the roles temporarily. If unavoidable, it's worth being explicit about the trade-off (actively watching for Scrum Master responsibilities quietly losing out to Product Owner pressure) rather than assuming the combination is cost-free.