The good news is that many of the smaller providers (where they exist - maybe your LTE provider is one?) are very excited about adding something like this to their network. Where the incumbents would rather just hide problems from you to keep you locked in, the smaller providers are very motivated to keep you on their network. They're often overworked and resource strapped - so a system that will help them narrow down the source of network problems and reduce truck rolls is usually very exciting to them.
You can easily determine how much of a problem it is in your case by calculating your bandwidth delay product: https://en.wikipedia.org/wiki/Bandwidth-delay_product
For many activities on the internet a 1,000ms latency would be intolerable, but for one-way video streaming it's unnoticeable to the end user. I don't really care if a packet containing video takes 50ms or 1000ms to get from the CDN to my TV, as long as it gets there and is reasonably consistent in it's ability to do so.
For this use case, if my machine can get 20Mb/s on the test, latency will just not affect me streaming a 10Mb/s video. Latency may be lowering my test results, but that's the point here - testing the effective throughput.