In order to find a path from Alice to Zoe, the path-finding mechanism needs to know the current capacity of every channel, namely the channel's initial funding minus the net amount of LN payments sent through it so far.
The path finder does not have to find an optimal path; any reasonable path would be OK. Therefore, it does not need to know the exact channel capacities. That is, if the net payment through a channel so far is 0.1275 BTC, it is OK if the path finder knows only that it is between 0.1 and 0.2 BTC.
Even so, the path finder needs to know of any payment that is large enough to change that approximate balance; or, if many small payments are made through the channel, it must be notified every time they add up to a significant amount.
Therefore, every time Alice makes a significant payment to Zoe, she must promptly notify the path-finding server(s) about it. If the payment went through a path of six hops, all six payments must be promptly reported to the path finder.
The current implementation, IIUC, has a toy path finding algorithm that runs on every node, and keeps track of the current state of every channel. Therefore, every node must be notified of every payment made by any user in the network. If there were a million nodes, each making one significant LN payment per day, each node would have to receive and process one million notifications per day. This is actually worse scaling than the original bitcoin network with SPV client wallets.
One could use a single central path finding server, or a few servers. Either way, any such server would have to know about every significant payment made by every user. So the original promise of confidentiality would be lost.
If some of those notifications are delayed or fail to reach a path finder, the latter will occasionally return a path that cannot, in fact, carry the desired payment. A failure rate of 1% may be high enough to drive users away.
Moreover, once the path finder has chosen a path, the selected middlemen nodes must "freeze" the relevant channels until the payment is negotiated and executed, or the negotiation fails.
The "path finding problem" is inventing an algorithm that would be decentralized, reliable, and scale better than the original bitcoin network. And would preserve the confidentiality of payments of the original LN concept. It is not obvious that such an algorithm will ever be found...
Zo mag je daar mijns insziens niet over denken. Dan zouden alle bitcoin millionaires wiens vermogen 75% in BTC zit ook alles moeten verkopen.