Before answering your question, we must review the mechanism of bleaching action. Hydrogen peroxide ($\ce{H2O2}$) is replacing other beaching agents as the preferred beaching agent in many applications. Although it was accepted that $\ce{H2O2}$ acts by destructively oxidizing colored organic molecules involved, its bleaching mechanism by such oxidation is still not well understood. However, recent works on the bleaching of textile by $\ce{H2O2}$ have identified that the hydroxyl radical ($\ce{HO^.}$) and perhydroxyl radical ($\ce{HO2^.}$) are the active oxygen species mostly responsible for such action [1]. The facts found by a separate study on the effects of the $\ce{HO^.}$ radical and $\ce{H2O2}$ on tooth bleaching suggest that $\ce{HO^.}$ has the main role in tooth bleaching with $\ce{H2O2}$ [2]
Suggested path for formation of $\ce{HO^.}$ and ($\ce{HO2^.}$) radicals from aqueous $\ce{H2O2}$ is as follows:
$$\ce{H2O2 + H2O <=> HO2- + H3O+}$$
$$\ce{HO2- + H2O2 -> HO2^. + HO^. + HO-}$$
Now, we look at bleaching process in Dentists' office: Stable hydrogen peroxide-urea solid is commonly used in these situations to avoid unstable aqueous $30\%~\ce{H2O2}$. It is described in Wikipedia article on hydrogen peroxide - urea as follows:
Hydrogen peroxide-urea (also called Hyperol or artizone) is a solid composed of equal amounts of hydrogen peroxide and urea. This compound is a white crystalline solid, which dissolves in water to give free hydrogen peroxide.
In the Wikipedia article on tooth whitening mentioned in your question states that:
The bleaching agent is either carbamide peroxide, which breaks down in the mouth to form hydrogen peroxide, or hydrogen peroxide itself. The bleaching gel typically contains between 10% and 44% carbamide peroxide, which is roughly equivalent to a 3% to 16% hydrogen peroxide concentration. The legal percentage of hydrogen peroxide allowed to be given is 0.1-6%. Bleaching agents are only allowed to be given via dental practitioners, dental therapists and dental hygienists.
At a dentist's office, they may use the light source to accelerate (and light-influenced catalytic radical cleavage) above spontaneous reactions to generate $\ce{HO^.}$ and ($\ce{HO2^.}$)Radicals. To support my argument, I'd like to point out the following statement from the same source you noted above in the Wikipedia article on tooth whitening:
Use of light during bleaching increases the risk of tooth sensitivity and may not be any more effective than bleaching without light when high concentrations of hydrogen peroxide are used.
Thus, use of light source is not a gimmick. It is a necessity.
References:
The mechanism of hydrogen peroxide bleaching: J. Dannacher, W. Schlenker, Textile Chemist & Colorist, 1996, 28(11), 24-28.
Effects of the Hydroxyl Radical and Hydrogen Peroxide on Tooth Bleaching: K. Kawamoto, Y. Tsujimoto, Journal of Endodontics, 2004, 30(1), 45-50 (DOI: https://doi.org/10.1097/00004770-200401000-00010).