The chain becomes valuable after breaking it starts feeling expensive.

Early in a streak, breaking it costs nothing, which is why so many end in the first fortnight. After a while the accumulated record itself becomes a reason to continue, and that reluctance to break it does real work on the days when nothing else would get you there. The chain has to reach a certain length before it starts helping.

Make the first few weeks as easy as possible so that you reach the point where the record matters. Keep it visible. Once losing it would genuinely bother you, the habit has become largely self sustaining.