Biden is hedging, instead of going all-in, because he's a smart politician.
First, Ukraine could still lose. Russia has a bigger population, more internal weapons production capability, China as an ally and weapons supplier, significant oil income, mind control over its people via a totalitarian grip on the media and internet, and nuclear weapons. Also, Putin is correct that we in the West with our goldfish-level attention spans are losing interest. If Ukraine loses, we'll see a genocide on the scale that last occurred in WW2. Putin could win the war in a matter of weeks if he was willing to hit Ukraine's cities with nuclear weapons. In any Ukrainian loss scenario, a Biden who went all-in would have lost the war for the Ukrainians - an incompetent commander in chief, but a Biden who did what he reasonably could while keeping his distance might be just as shocked as the rest of us, and we could relate to that. Yes, it is ridiculous people think this way, but have you been watching US politics long?
Second, a Biden who aggressively supports Ukraine leaves the Republicans in a position where they can only oppose the president's agenda. A more moderate approach is thought to maintain bipartisan support, and also theoretically give some Republicans an opening to take the opposite position and critique Biden for not doing enough. So far, only a handful of Republicans have taken strong anti-Ukraine stances, and they are the ones trying to tie Hunter Biden, who is not president, to a scandal from the Victor Yanukovyich days. This outcome can be seen as the most positive of all possible outcomes for Ukraine, though it may not last. When Trump is nominated, Vlad may call in a favor, and the very next day the entire Republican party will be against supporting Ukraine.
Third, Biden has negotiating leverage over Putin only to the extent and for only as long as he is not going all-in. Behind the scenes, diplomats are trying to make deals and NATO's only remaining leverage is the threat of sending the next package of tanks, missiles, or aircraft. The slow escalation in support... HIMARS, Abrams, ATACM, F-16s... can be seen as outcomes of a series of diplomatic discussions that did not yield NATO's preferred goals. The time to escalation can be seen as a tradeoff between giving diplomacy a chance and not letting the Russians stall the discussions for too long. Also consider... something has held Putin back from using nuclear weapons so far. I suspect there are diplomatic chess pieces in place preventing that move - for now.
Fourth, as Biden commits military resources to Ukraine, he has to watch his back in the Pacific. A Chinese attack on Taiwan or the Philippines might be provoked if China decides the US is over-committed in Europe. Particularly, the US would need as many missiles, drones, and aircraft as it could spare to defend Taiwan. If China ever got the impression resources were being diverted... that would be the time to strike. As if that wasn't enough, Iran could similarly sense a pinned-down US and open a third front in the Middle East.