I'd say they've improved the weaknesses but not eliminated them - even a A7R3 ($5300) still only has around half the rated battery life of many DSLRs (CIPA rating 650 shots vs 1230 for a Nikon D750 or 1840 for a D850). Having said that the old D7000 can do over 2000 shots on a charge with my use and its official rating is 1050, so if they beat their official rating by a similar amount its probably still heaps for most people and as you say it has other advantages with the smaller size and weight.
Similar story with the AF from what I've heard - it may not be as good at speed and tracking as the better Nikon and Canon DSLRS (which is part of the reason professional sports photographers are still almost exclusively using those) but its plenty good enough for most people now.
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