So far, no one has mentioned the optimum length of tubes to get high efficiency.

It is agree that tubes provide direct path way for electron transport to reach conducting oxide substrate, but inner surface area is less compared to nano particles. Hence amount of dye adsorption is low, consequently efficiency is less.

The best optimized thickness in the nanotubes is 0.5 - 0.6 micro meter. With this parameter highest efficiency achieved is 9.4% in case of perovskite solar cells. In case of DSSC which is 7.6% with electrochemical deposition of thin films.

1. your first statement "By increasing the length of titania nanotube arrays (fabricated by anodization method), the total effective surface area increases which will increase the photons absorption rate." is not fully corrected. light absorption has nothing related to the surface area but determined by the absorption coefficient (materials related), transmission loss (thickness related) and reflection loss (refractive index related). the reflection loss may be reduced by nanotube because of the gradient refractive index because the diameter of nanotube is smaller or close to the light wavelength. the transmission loss can be reduced by increasing the length of your nanobute (but not the surface area although the surface area is also increased simultaneously). 

2. In the photoelectrochemistry of pure TiO2 nanobute (without dye), the minority only need to migrate a short distance to the electrolyte (maximum the half thickness of the wall of your nanotube) and the majority have to migrate axially to the bottom of nanotube. however the conductivity of the majority is normally high, so the length will not affect the resistance too much. a few years ago, people find exciton in TiO2 nanotube under excitation and assign it as the reason of lower diffusion/drift rate.