I actually own a Fire HD 8 2016 and I have to say the answer to your question really depends on what your expectations are.
Many people think of Fire Tablets as walled gardens, locked into the Amazon ecosystem. And while that might have been true with previous generations, it is not the case with the current Fire tablet line.
Maybe I'm just not as fussy as some, maybe I'm enamored with how much I am getting out of the purchase given the price I paid, but I'm actually very happy with my Fire HD.
I've installed Google Play (*without Root) on it and it downloads/installs/runs apps from the Playstore without a hitch. Granted there may be exceptions, it's not like I've tried every app there is available out there but so far I've had no problems. A brief list of things I'm currently using include: Firefox Sync, Solid Explorer, Pocket, Airdroid, MX Player, Reddit, Netflix, even tried Kodi for abit (It worked, but I didn't know how to configure it).
One thing I know for fact it has trouble running is custom launchers. A workaround is needed and even then it ends up "glitching" for about a half second as shown:
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The main issue most people have with owning a Fire HD tablet is as you might imagine. It runs proprietary OS based off Android and it comes with bloatware just as many cellphones. Think SenseUI, MIUI, Samsung TouchWiz, whatever. It's Android, but different. Root? Depends on model and software version. Not all Fire Tablets can be rooted.
So if you're the type that immediately roots, installs custom launchers on your phone to get that STOCK android feel that you will not compromise on then the Fire HD is NOT for you. If you usually just use your phone AS IS? Then it's time to consider what you are getting for the price. Decent, well-built, no-frills hardware. 4G? Nope. Super camera? Nope. AMOLED display? Nope. But spec-for-spec it would be hard to find anything for anywhere near the same ballpark in price.
Basically what I'm saying is IF you are just looking for something that serves a purpose on a budget and the few drawbacks are not a deal breaker for you? Then MAYBE go with a Fire HD and it might end up pleasantly and surprisingly exceeding your expectations.
**TL;DR:
Fire HD Pros: Value for money device. Runs playstore.
Fire HD Cons: Non-stock interface, cannot root, custom launcher "glitches".