Ketenes cycloadditions, avoided

The advantage of using the photocycloaddition of pentacarbonylcarbenechromium complexes over the ketene cycloaddition method is the absence of ketene dimerization and the avoidance of use of excess alkene in the former method. Also, the mild reaction conditions associated with the use of chromium carbene complexes avoids epimerization and thermodynamic equilibration of 2-monosubstituted cyclobutanones. 

However, at first sight, ketenes (358) seem to be avoiding the higher coefficients. We have already seen on p. 143 that they can undergo [2 + 2] cycloadditions in an allowed manner, but we also have to account for why they do so, even when a [2 + 4] reaction is available. A [2 + 4] reaction would involve... 

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