With direct electrification at the core of global decarbonization efforts, it is key for policy makers to adequately evaluate market dynamics in renewable power systems. The ongoing integration of renewable energy sources fundamentally changes these dynamics, with variable production profiles, lower marginal production costs and increased price volatility. This motivates us to study how an increasing supply from renewable energy sources impacts decision making of intermittent and non-intermittent producers in sequential forward and spot markets. We do this by examining prices and volumes observed in an experimental trading environment that allows us to vary the market share of intermittent renewable energy production with a high degree of control. The results show that non-intermittent power producers, who can flexibly adjust volumes in the short-term, can retain their profits by moving focus from forward to spot markets. We find empirical support for our experimental results by validating data from German short-term power markets in 2021 and create awareness on the convenience yield for flexibility in power systems with a high market share of intermittent renewable energy sources. The study thereby guides policy makers to align supporting the uptake of intermittent renewable energy production with taking away hurdles faced by low-carbon flex technologies.