The promise of "free and open" multi-terabyte datasets often collides with harsh realities. While these datasets may be technically accessible, practical barriers -- from processing complexity to hidden costs -- create a system that primarily serves well-funded institutions. This study examines accessibility challenges across web crawls, satellite imagery, scientific data, and collaborative projects, revealing a consistent two-tier system where theoretical openness masks practical exclusivity. Our analysis demonstrates that datasets marketed as "publicly accessible" typically require minimum investments of \$1,000+ for meaningful analysis, with complex processing pipelines demanding \$10,000-100,000+ in infrastructure costs. The infrastructure requirements -- distributed computing knowledge, domain expertise, and substantial budgets -- effectively gatekeep these datasets despite their "open" status, limiting practical accessibility to those with institutional support or substantial resources.