Could LN wallets be seamless? Currently, the funds deposited in a payment channel cannot be sent on-chain without closing the channel. Similarly, the user must open a brand new channel in order to deposit some on-chain funds into LN.

Is it possible to make a LN wallet seamless, so that the user could be freed from dealing with hassles like channel opening/closing?
No, that is not possible. The opening and closing of channels by confirming funding and closing transactions represents the act of securing and delivering of the channel capacity and balance respectively.

The 2-of-2 multi-sig from the funding channel represents the total channel capacity. During the lifetime of the channel, this multi-sig must remain unspent, so that the spending transaction which is eventually confirmed during channel close can be updated during the channel lifetime. 

Since no coins can be created, the (funding) input cannot be more than the total of closing transactions outputs, whose amounts represent the last channel balance.

There are proposals to "spend" this funding output together with additional inputs/outputs to an updated funding output to update channel capacities.
See channel "splicing" on this topic.