The honest answer is that equipment access changes how a plan is written, not whether it'll work. A well-coached dumbbell-only program can build real strength and muscle; a poorly run barbell program in a fully loaded gym won't outperform it just because the equipment looks more serious.
What a commercial gym mainly buys you is exercise variety and the ability to load heavier compound lifts more directly — useful for advanced strength goals, less critical for general fitness or early-stage hypertrophy work.
A home setup forces more creativity: tempo changes, unilateral work, and higher rep ranges often substitute for heavier loading when equipment caps out. None of that is a downgrade — it's a different toolkit aimed at the same outcome.
This is exactly why intake forms ask about equipment access before a single session gets written. The plan adapts to your situation rather than assuming a fully stocked gym you may not have.