Quite right that this is not a solution as such ... in terms of my bus analogy getting a transaction "accelerated" simply means that next time the ViaBTC bus arrives it will allow your transaction on board instead of the transactions that are first in the queue. Of course it will break down if too many uses the "accelerator".
Still it has saved the day for quite some people until now - because sometimes it really is critical to get a confirmation on a transaction you expected to get confirmed yesterday already.
If you have an inbound transaction into i.e. Mycelium, or an outbound "partial" transaction from a wallet like Mycelium, there is another trick one can do - "Child Pays for Parent" - make another transaction and slap a high fee on it. The chain of transactions will most likely be confirmed within some few blocks. This won't work if you're receiving funds into your Localbitcoins wallet for instance, then there is nothing to do but wait ... or eventually, try and use that "accelerator".
There is the third way; arguably the best, but it requires that the sending wallet supports it in the first place, and that the feature is enabled: RBF, "Replace by fee". With RBF, one can change a transaction after it's sent as long as one applies higher fee - i.e. optimize the transaction by including more recipients or higher amounts (instead of sending multiple transactions), add higher fees to get it processed faster, or ... revert the transaction. Due to the last possibility, RBF is a politically hot potato - normally one can be reasonably sure that a transaction will get confirmed sooner or later, one can trust a 0-conf, but when the RBF-flag is enabled on the transaction, the sender can take the funds back.