As generative AI tools like ChatGPT become integral to everyday writing, critical questions arise about how to preserve writers' sense of agency and ownership when using these tools. Yet, a systematic understanding of how AI assistance affects different aspects of the writing process - and how this shapes writers' agency - remains underexplored. To address this gap, we conducted a systematic review of 109 HCI papers using the PRISMA approach. From this literature, we identify four overarching design strategies for AI writing support: structured guidance, guided exploration, active co-writing, and critical feedback - mapped across the four key cognitive processes in writing: planning, translating, reviewing, and monitoring. We complement this analysis with interviews of 15 writers across diverse domains. Our findings reveal that writers' desired levels of AI intervention vary across the writing process: content-focused writers (e.g., academics) prioritize ownership during planning, while form-focused writers (e.g., creatives) value control over translating and reviewing. Writers' preferences are also shaped by contextual goals, values, and notions of originality and authorship. By examining when ownership matters, what writers want to own, and how AI interactions shape agency, we surface both alignment and gaps between research and user needs. Our findings offer actionable design guidance for developing human-centered writing tools for co-writing with AI, on human terms.