Role of Bypass line - Blowdown Valve

The role of bypass line can not be for making balance up and downstream of BDV when there could be high delta p?

I think your interpretation is based on your observations of by-pass valves around big isolation valves in process applications. For BDV, we dont’ want to pressurize downstream system (e.g. flare header). But you need to understand fundamental aspect of your query.

Any kind of pneumatic valve (control valve or BDV or ESDV), has “actuator” which is designed considering the maximum dP across the valve at any time. When you have high dP, relative size of actuator is higher compared to the valve having lower dP across it.

In case of BDV, process datasheet must specify maximum upstream pressure and the downstream flare header pressure. Based on this values, actuator would be designed in such a way, that we don’t need to pressurize downstream system before opening.