You are making a couple of incorrect assumptions:
-You do not have to apply for an app-o-rama every 3 months. You not only do not, you likely cannot do so. You'll need to wait 12-18+ months for some cards, and for others you may never again be able to apply for them.
-You do not need 100k in one program. You also have the possibility of using two one way awards from two different programs.
-It is hard work to do any of this.
-You can gain 0 miles right now by doing absolutely nothing, or gain 50,000-100,000 with a little bit of work. So if you prefer to do nothing and have no miles, good. But you need to add a value to the miles. When you discredit them as having no value then it is easy to say things like getting "rid" of gift cards is overwhelming. Remember your goal is a $4,000 flight.
If you do the following then it is not a zero sum game:
Deposit $5k in bank account.
Buy gift cards to cover minimum spending -$3k
Pay off $3k Credit Card bill from bank account
Now you have an asset--$3k in gift cards, and no liability.
Each time you use the gift card deposit a matching amount back into bank account. if you spend $100 a week, deposit $100. Yes this will take you 30 weeks to pay yourself back. In the meantime you'll earn many miles because you have hit the minimum spending.
Examples:
#1- Apply for 2x AA cards and you'll have 106k AA miles. $6k purchases in 4 months. Using the above this would take you 60 weeks to pay back at $100 a week.
or
#2 Apply for 1x Chase MP explorer-55K after $1k spend
Apply for 1x Chase Sapphire Preferred 40k after $3k in spending.
You will have 98k United Miles, and will take 40 weeks to pay yourself back.
One year later do the other example for your next trip.