There are plenty of wallet's available for free that you can use which are also safe to use as well, Myetherwallet, Coinomi, etc. both can hold and store many multiple Crypto's , Exodus is not your only choice.
Exchanges exist because they make money from you, this is just a fact of life and something you need to adjust to and research and prepare for. Unfortunately there is no way out of paying fee's when you enter into such realm's. It is just a cost of doing business with them just as exchanging Crypto's in Exodus.
Bitcoin cost's a huge amount to transfer or send anywhere compared to many other Crypto's, it is also high priced when using it on an exchange as well, so, maybe use LTC or ETH instead to cut cost's there instead.
Binance has minimal fees if you hold some Binance on the exchange to use for fee's, LTC and ETH are also much cheaper to use when transferring funds too, so just convert to those which are cheaper to use when doing transfers to your wallets, and then sit and hold until the cost's come down relative to what you want to hold.
BTC seem's intent on charging as much as it can, which in the end will be it's demise among'st the average user... So move on to Crypto like ETH and LTC instead when using trading platforms.
It is easy enough to time your trades up to BTC when the comparative price gap between, LTC, ETH, etc occurs. Never rush, all of these crypto's cycle through up's and downs all the time, crashes occur with great frequency, but the momentum is nearly always to the upside over time.
Give this a bit of thought.........., out of 7+ Billion people on the planet right now, you are 'one' of only about three million that are aware of or are involved in Crypto right now.
What happens when just a hundred million out of that 7 billion get on board the Crypto experiment, and why are the banks and Fiat exchanges scrambling to catch up right now ?
Learn all you can while the rest of the population is just discovering and finding out about it, get ahead of the curve, research, research and research all you can, What is Blockchain for a start ? Do you know what it is ?
Get educated about what it actually is, and what the differences are between the different Blockchain alternatives.
How does Iota differ from Ethereum, Litecion from Bitcoin, Eos from Veritasium ? Learn about all this 'BEFORE' you put a single cent into any of it first.
If you don't then you are just gambling your money away.
It only takes a little while of your time to get a grasp of it all, and then a few hours more before your mind is blown wide open by the potential of it all.
And then just a few minutes before you are ready to blow your life savings on the newest ICO or the latest hottest Crypto on Coinmarketcap.
Only to see it plummet by 200% in a week and wipe out all of your 'so called investment' .....
Shit happens, every week, time after time after time.
There are fortunes ready to be made, but people need to do their own research on it all, the whole lot from go to Woe.
At least 95% of all current crypto's will fail or be shut down by .Gov.com, Enter at your own Risk!