The better option is to have the client automatically CLEAR Summoner Spells every time you first join a lobby and prevent you from selecting your Summoner Spells until immediately after you lock in your champion.
It would produce a more consistent Champion Select process and eliminate the possibility of forgetting or not checking your sums.
I'll break my idea down below. If you want the "TL;DR", stop reading now.
Definitions:
"Optional" - players will NOT be kicked from the lobby if the timer runs down and they have not confirmed a selection
"Mandatory" - players WILL be kicked from the lobby if the timer runs down and they have not confirmed a selection
"Existing feature" - the feature being discussed is live as of Patch 6.8
"Proposed feature" - the feature being discussed does not exist as of Patch 6.8
PROPOSED CHAMPION SELECT PROCESS
● Champion "intent" pick phase
•Optional
• Existing feature
● Ban phase
• Mandatory
• Existing feature
● Champion "lock" phase
• Mandatory
• Existing feature
● Summoner Spell select phase
• Optional
• Proposed feature
• Immediately after locking in your champion a "Summoner Spell Select" window appears covering up the lobby/Champ Select window
• The "SSS" window appearance is accompanied by an audio que and contains text telling the player to choose two Summoner Spells
• The "SSS" window displays all unlocked Summoner Spells as large icons (as large or larger than the Champion icons)
• The "SSS" window "minimizes" once the player confirms Summoner Spell choices or if the timer runs down or if the player manually minimizes it
• The window can be reopened any time after initial confirmation
• Prior to the initial appearance of the "SSS" window, the player would NOT be allowed to select Summoner Spells or minimize/maximize the "SSS" window AND the Summoner Spell "slots" would be blacked out
● Champion Select continues as usual.