I think Aleksei would've make a good Tsar, who could act according to the truth, about what was really going on, not like his father who didn't want to change things, because it always has been like that in the past, or because he didn't bother to see if what he was told was true.
As for Aleksei's sickness, and the strong possibility that he would die young (and not doing much), just think about Baudouin IV, the King of Jerusalem (1180's); he was a leper, and died at 25 years old. But he reformed his kingdom, prepared it's defense against sultan Salah-ed-din (Saladin), and even won a great battle. He had sisters that would take his succession, but they made bad choices of husband, and the kingdom was lost.
Aleksei was in a similar situation; his kingdom was in turmoil, with enemies close and within, but with a regency at first, and with necessary reforms, and the establishment of a constitutional monarchy, his reign could've been the remedy Russia needed to stabilize. Do remember that when Nikolaï abdicated, the Provisional government expected a Regency, and Aleksei as Tsar, and were accepting the idea. The Russians and the Duma were mostly sick of Nikolaï doing nothing for them.
Aleksei was popular a few months before; think of the Russians reactions when they were seeing him:
The Heir! The Heir! And they wanted to touch him, speak to him, etc. Methinks the Bolsheviks were much more afraid of Aleksei than Nikolaï going on the throne.
As for the influence of his mother, I think a Regency would've cut it very quickly! Do remember that the only thing that stopped them from sending Alix in a convent was Nikolaï; with him gone, I sadly think that Aleksei would rarely have seen his mother again, and his father for that matter. That's why Nikolaï abdicated also for his son (though it was illegal), as we all know.
Well, that's my two cents!
