I've played a little of Fire Emblem Heroes now. The smaller battlefields are quite simplified, but I think that's the point, it's a causal game designed for short bursts of play. Also, the fixed screen battlefields mean that you can swipe the battlefield to move characters, which would be difficult to implement if the battlefield was larger than the screen. I tried the iOS port of Shining Force which used a virtual D-Pad and it was very fiddly; the control scheme of Fire Emblem Heroes feels very well thought out.
Like Super Mario Run, Fire Emblem Heroes is a stripped down version of other games in the series on the 3DS or consoles. The message is clear in both cases: if you want the full experience, buy a Nintendo system. I don't really mind given that it's free (hopefully microtransactions won't feel necessary - so far they haven't) and I don't have the time for longer games anyway.