Assume the lightning network wants to support 100k payments per second globally.
Now every time a payment is attempted, aborted or settled the balance of almost every channel in the payment flow changes. Assuming 5 channels being involved in a payment (and assuming no failed payments as the balance values would magically instantly known to all peers) this would still result in 1M messages that would have to be broadcasted to every participant in the network per second.
Assuming 100 Bytes per message (as we have not only the balance value but timestamps, shortchannel ids, signatures to prevent spoofing and hmacs) this would be at least (!) a datastream of 100 MByte /second for every participant wich is almost 1 Gigabit/sec
Even if the internet would not break if every participant was constantly requiring such a throughput the nodes would have to be able to processes all that information. A regular webserver on commodity hardware can handle up to 10k http requests per second. So also the nodes would have some serious challenges.