I would like to know why most TauDEM specialized tools have been developed just for the D-Infinity flow model. Is it because the D8 would not make sense for these algorithms, or they just have not been implemented? In the first case, what is the reason?
Mostly this is a matter of implementation. They have not been implemented. Typically, each tool was historically developed in for a specific project or purpose and this development process has not resulted in complete consistency in the functionality available. I think all the algorithms would make sense with D8 too. Two of the tools (DinfAvalanche, DinfDistUp) have a parameter that sets a threshold for flow proportions to use in the accumulation. Setting this threshold to 0.5 (or 0.499 to numerically be >= 0.5) gives a result equivalent to D8. This could be added to each tool (given time and funding), and it would be good if there was a systematic process of upgrading each tool to include this threshold parameter so that equivalent D8 options are available to users.
If there is a developer who wants or needs this, these tools with an existing threshold could be used as a guide for implementation of others. A fork and pull request in the github repository (https://github.com/dtarb/taudem) could be used to request inclusion of code changes in the official releases.