That last part is one of the main problems of Arena imo, also correlates with 'sniping', hence the possible solutions offered in this and other topics such as rating decay.
Arena is not showcasing the ranking over the entire season but indeed more from the last x-games of given player.
It's more about 'who gets the best streak' than performing during the entire season.
With 'simple games' you have,imo, more incentive to play. Like you can allways try to get higher in ELO. This ranking is more visible to other players (more rewarding if you like this) and offers the possibility to really play with players from your strenght (restrict table acces based on rating). This way the random/variance doesn't hit as hard, and you will get a closer ranking matching your skill level than your Arena ranking.
In Arena you only have the possibility to filter on league, this is somewhat helpfull at the beginning of the season. But for popular games a few weeks in the season this means you have at least 400 arena points between 1st and 'worst' player, making it very hard to climb in elite (if you hit a good streak and position, very very low reward to continue playing). When you look at ELO scores, by this time you are facing people with 100 ELO in Elite league.
I still like Arena mode, but it needs some tweaking.