Using Standard Edition for a VLDB
Here is my two cents in the form of an answer...

Kin pointed out the CPU and memory limitations of standard edition (16 cores/4 sockets and 128GB - though see Buffer Pool Extension), which I completely agree with being the largest obstacle. If you're server is going to be under those requirements then it's a moot point.

Aaron pointed out that if you use SQL 2016 you'll get a less flexible form of AGs. Honestly, to me, it doesn't sound like this will work for you. Cheap storage would be the death of it and if you're considering standard edition I highly doubt this database is that important. Not saying all important databases need to be enterprise edition - but the fact that you're in cheap storage and looking at SE says it all.

Additionally you're not looking at any enterprise level features which could help you. Range partitioning the key/value pairs, compression, column store indexes on the KVPs, TDE/AE, etc.

So, it seems, at the end of the day you're looking for someone to talk you INTO using enterprise edition. I don't know what the usage patterns of the database are, the load, or what it supports for the business... so unless it requires more than the CPU/Memory of standard edition I see no need with the information provided to go with enterprise edition.

The last thought is if this will be virtualized - if so, depending on licensing (enterprise of the host[s]) that's where it may make sense. This wasn't included in the discussion so I'm just throwing it out there.

See also: Features Supported by the Editions of SQL Server 2014