I personally wouldn't re-use yeast that had fermented a 1.070 beer. 1.060 is about the upper limit here, thought there is a bit of grey area as far as how high is too high. The higher the OG, the more stress the yeast have endured. I like to limit it to the mid 1.050s myself. This applies to both direct pitching and washing.
As far as flavors carrying over, yes, it can happen. I don't think it's so much "bad" flavors, but rather undesirable flavors. If you use yeast harvested from an IPA or IIPA to ferment a less flavorful style, you could bring some flavors from the hops that you may not want. This also applies to both direct pitching and washing.
So, how do you get around all of this and still reuse yeast? Fortunately, it's not at all hard. I do it all the time. I also NEVER wash yeast because it's a pain in the arse and there are much easier ways to get clean yeast.
To have clean yeast for your yeast bank, instead of washing, make an oversized starter and save a little (25-50B cells) in a sanitized mason jar to be used for another starter later. This will give you clean yeast that has not been stressed by fermentation and has not been exposed to hops.
To minimize the number of starters you need to make, plan your brews so that you do a lower OG, less hoppy brew first to be followed with a bigger or higher IBU beer afterward. This will allow you to direct pitch slurry without having to be concerned too much about yeast health or unwanted flavors carrying over. You can also do this with dry yeast, rendering a starter unnecessary.