Most young neutron stars belonging to the class of Central Compact Objects in supernova remnants (CCOs) do not have known periodicities. We investigated seven such CCOs to understand the common reasons for the absence of detected pulsations. Making use of XMM-Newton, Chandra, and NICER observations, we perform a systematic timing and spectral analysis to derive updated sensitivity limits for both periodic signals and multi-temperature spectral components that could be associated with radiation from hotspots on the neutron star surface. Based on these limits, we then investigated for each target the allowed viewing geometry that could explain the lack of pulsations. We estimate it is unlikely ($< 10^{-6}$) to attribute that we do not see pulsations to an unfavorable viewing geometry for five considered sources. Alternatively, the carbon atmosphere model, which assumes homogeneous temperature distribution on the surface, describes the spectra equally well and provides a reasonable interpretation for the absence of detected periodicities within current limits. The unusual properties of CCOs with respect to other young neutron stars could suggest a different evolutionary path, as that proposed for sources experiencing episodes of significant fallback accretion after the supernova event.
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